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Home > Science Worksheets > Scientific Method

The series of worksheets you will find in this section will really test your understanding of the concept of the scientific method. You will be put to the test in many diverse scenarios. We start by learning the order of the steps of process and the history of how value was attributed to this process. We learn how to form and write valid hypotheses. We learn how to identify and classify variables that can affect the outcome of an experiment. Students will learn how to keep all conditions in the environment the tests are taking place to limit inaccuracies in our data collection process. We learn how to identify a control and decide upon proper experimental groups that should be tested through the course of this. We learn how to collect data and then analyze that data through the use of data tables and charts. From that data analysis we then learn how to draw acceptable and valid conclusions while taken all things into considerations.

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Provide the letter of the definition that matches the scientific terms below.

Starting the Process

The scientific method is basically an organized way to investigate something that interests you, when you want to find out why something happens the way it does. It all starts with a question.

The Process Page 2

After scientists complete an experiment they report their conclusions. Each branch of science has a report format for publishing the results of experiments. If you do an experiment for a science fair project you will report your conclusions on a poster board for everyone to see. Y

Understanding the Process

Put the step number next to each step of the scientific method for this problem.

Practice with the Method

In 1872 a wealthy railroad tycoon named Leland Stanford (Stanford University is named after him) made a bet with a friend about a galloping horse. Put the step number next to each step of the scientific method for this problem.

Historic Process of the Method

Gregor Mendel was an Austrian monk who lived from 1822 until 1884. He performed some of the first research ever in heredity. Mendel grew an estimated 28,000 pea plants over eight years. Students can perform an experiment that is similar to one of his famous experiments with pea plants.

Understanding Hypotheses

A hypothesis is testable if you can create a controlled experiment that will give you more information. This hypothesis is testable because you can experiment with two groups of plants of the same species.

Practice with Hypotheses

Write a testable hypothesis for these situations. The beauty of this worksheet is that there are a ton of different approaches that you can take.

Hypothesis Practice

Have another go at these types of questions.

Understanding Dependent and Independent Variables

Experiments test the influence of one thing over another. A proper experiment compares two or more things but changes only one variable or factor in the experiment.

Identifying Dependent and Independent Variables

Identify the dependent and independent variables in the following cases.

Practice with Dependent and Independent Variables

Exercises with dependent and independent variables, understanding control and experimental groups.

The way to show that a hypothesis is true or false is to design and complete an experiment.

Identifying Control and Experimental Groups

Identify the control and experimental groups in the following cases.

Practice with Control and Experimental Groups

Exercises with control and experimental groups.

The control group does not get the factor being tested. The experimental group does get the factor being tested.

Writing Experiment Conclusions

The conclusion gives a snapshot of what you accomplished so it contains summary information about the experiment as well as the conclusions.

Identifying Experiment Conclusions

Write one sentence to the right of the graph that summarizes what the data shows in each of these experiments.

Practice with Experiment Conclusions

Exercises with experiment conclusions, exercise set one.

Researchers at Pur-Rite Pharmaceutical Company also developed a new additive for cattle feed that they hope will cause beef cattle to gain weight faster so they can be sent to market sooner.

Exercise Set Two

The executives in charge of advertising for Big Spill brand of paper towels want to advertise that Big Spill towels absorb twice as much water as Good Buy brand.

Exercise Set Three

In a taste test consumers preferred Healthy Meal brand frozen enchilada dinner over the other best-selling brand.

Exercise Set Four

If you make ice cubes from warm water the cubes freeze faster than if you made them from cold water.

Exercise Set Five

The vacuum seal method of storing chicken in the freezer results in less freezer burn than storing the chicken in a freezer storage bag.

Stroop Effect

What happens if you ask someone to name the color of letters printed on a flash card if the letters spell the name of another color?

Scientific Method - Inertia and Momentum

A basic scientific principle is that a body in motion remains in motion unless stopped by an outside force and a body at rest remains at rest unless moved by an outside force.

Effect of Light on Fall Leaf Colors

Do leaves need sunlight in order to change color in the fall?

Water Absorption in Plants and Flowers

How do plants absorb and use water?

Iron and Magnetism

Swish the magnet through the cereal mixture making certain that the magnet reaches the bottom of the bowl because the iron will sink to the bottom.

Oxidation of Cut Apples

A cut apple turns brown after a few minutes. People don't like to eat brown apple slices but you'd like to serve cut up fruit to your guests who are coming in half an hour.

Oxidation of Cut Apples by Variety

Form a conclusion from what is presented.

What Is the Scientific Method?

Scientists use many methods to uncover evidence and draw conclusions, but the scientific method is at the root of all experiments. This method is a guideline that aids people in testing their ideas and finding evidence that can show us the relationships between things, forming the foundation of discovery.

It is a means of using experiments to solve a problem or answer a scientific question. It includes doing experiments, gathering information, and then making conclusions about what you have discovered.

It is a fundamental scientific concept and is the basis for all scientific discoveries. So, let's discuss what the scientific method entails and go through the steps to understand how you can test, examine, and draw conclusions about the world around us.

This is a process that can help you in all walks of life, not just in a science lab. The basic overview of the method requires you first to identify a problem or truth that you are seeking. It could be something as simple as "does water help plants grow?" After you determine the problem you need to come up with a prediction of what you think the answer to the question is. After that we design an experiment to test this prediction. After we gather all the data from the experiment, we examine the data and draw a conclusion. From there we share and discuss all the data with others.

An Explanation of the Six Steps

No matter what your problem or question is, whether it's something small or something big, the scientific method always makes use of the same six steps:

• Ask a question.
• Research the topic.
• Form a hypothesis or testable explanation.
• Test with an experiment.
• Analyze the data.
• Draw a conclusion.

Let's take a closer look and go through the scientific method together.

1. Ask a Question

This first step is where you get to ask any scientific question you want an answer to. Keep in mind the question needs to be something you can test. The questions typically begin with how, what, where, when, who, why, or which.

For example, "how can I make a plant grow faster?" or "when was the universe created?" The latter question would be pretty tricky to answer, but the first one is testable! Once you have your question, you can move on to the next step.

2. Research the Topic

You'll need to have some background information to test something. The more you know about a subject, the easier it will be to conduct the experiments and come to your conclusions. Not doing research could result in mistakes that might skew the data you collect during your investigation.

3. Form a Hypothesis or Testable Explanation

Forming a hypothesis (an educated guess) is when you predict what you think will happen using all the information you have gathered so far.

For example, it is reasonable to assume that "plants that have fertilizer in the soil will grow faster than those without." Now that you have predicted what will happen, it's time for the fun part - the experiment!

4. Test With an Experiment

You will need to design an experiment to test if your hypothesis is correct. In other words, this is when you figure out if you're right or wrong.

There might be multiple tests you need to do to come to the correct conclusion and ensure you didn't get there by accident. If you're running many trials, it is better to change only one variable at a time, which allows for the highest level of accuracy.

5. Analyze the Data

Once your experiment is complete, you'll need to analyze all the data you have gathered. You can do this using graphs, charts, diagrams, etc. This charting aims to find out if your hypothesis is supported or contradicted. If the experiment results don't support your original theory, you can change your hypothesis and run more tests.

6. Draw a Conclusion

Conclude whether you accept or reject your hypothesis. In many cases, the experiment will not support your theory, but that's okay – you can start over with a new understanding of how things work.

The last thing that needs to happen is to communicate your findings. You can do this by writing a report or giving a talk on the subject.

In short, the scientific method is an excellent way to study and learn things while getting to do fun and exciting experiments! Whenever you have a question about science, nature, or even the universe, you can always follow these six steps to find the answer, or at least get one step closer to finding it!

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Scientific Method Worksheets

All savvy scientists conduct experiments using the scientific method. This method allows for different observations to take place in order to prove one's theory in regards to the nature of science. It is important that students understand that they must investigate their theory by testing out their hypothesis. Untested theories have no substance in the real world.

We offer a wide variety of worksheets dedicated to helping students learn all about the scientific method. Once they understand how this truth seeking method works, then you can incorporate experiments into your lesson. We have tons of exciting science experiments for you and your class to test out. They are interesting, fun, and surely a crowd pleaser.

The Scientific Method is a series of techniques used to examine phenomena. This methodology date back to third century BC The primary goal for the use of Scientific Method is in truth seeking. We provide students with a series of worksheets below to introduce them to the basic process.

• Adjectives to Describe a Problem - Write an adjective on each line to describe a problem.
• Adjectives to Describe an Hypothesis
• Adjectives to Describe a Well Written Conclusion
• Influential Scientists Worksheets
• Scientific Method Outline
• Science Rubric Makers
• Steps of the Scientific Method - Can make for a nice class poster or the front of a binder for students.
• Lesson Plans
• Teacher Resources

Printable Science Labs That Use and Apply the Scientific Method

• Battle of the Spheres
• Cool Down, It's Just Water!
• It's Just a Phase They're Going Through!
• Jelly Bean Graph
• Jelly Bean Record Page
• Jelly Bean Sort
• Introduction to Populations
• It's Coming To Me!
• Now that's Phun!
• Now that's using your head!
• One, Two, Three Isaac Newton and Me!
• Time to lend NASA a hand
• The Biochemical Guessing Game!
• The Dissolution Solution!!
• What's going on here?
• Who needs Bell Atlantic?
• WOW, That's Hot and Cold!

What Is the Scientific Method?

The scientific method is a simple way of researching. Everyone can use this method to prove something they think is true. Scientists use this method when they are studying different things in the world. Learning about the scientific method is essential so you can find the answers you want to a question. You need a lot of information to use the scientific form! This information is called data.

Scientific Method Steps

There are 7 steps of the scientific method. We will take a really deep dive into this later on, but for a brief overview: The first thing that researchers do is that they gather a lot of information about a topic. For example, a scientist studying one plant will collect a lot of information about it. Then they will look for a reason to explain why the plant does a particular thing. The reason is called a hypothesis. The hypothesis is not enough. To convince people that their answer is the right one, they have to experiment. The experiment will try to prove the hypothesis. The results of the experiment will be collected and presented. These results will show if it was correct or not. Everyone can use it at home to prove a hypothesis.

Look Around You and Observe

The first step is to look around your house. Can you see anything interesting happening? For example, notice how it turns dark outside at night.

Think of a Question

Suppose you noticed that it turns dark outside at night. You now have a question that you formed from this observation: why does it turn dark at night?

Predict an Answer

Based on your observations, you can predict an answer. For example, it turns dark at night because there is no sun to light up the sky. This is your hypothesis. You will now have to prove that it’s true. Otherwise, how will people believe you?

Experiment to Find Out

Now you have a hypothesis so you can experiment. An experiment has to be perfect, so it is accurate. Make sure that there is at least one constant in your experiment. For example, you can check whether or not the sun is up. Make sure you check at two fixed times in the daytime and at night. This way, you can observe the effect of the sun on the darkness of the sky.

Write Down the Results

You will have to record whatever results you find. Note down anything else you see as well. These results will show you if your hypothesis is correct.

Did You Predict Correctly?

After gathering results, you can write down all the results to see if they make sense. If you predicted that the sun would make the sky bright, the results would show that it was sunny in the daytime when the sun was out, but it was dark in the nighttime when the sun was gone.

Where Did the Scientific Method Come From?

Many scientists have contributed to the scientific method. Some famous scientists like Isaac Newton also wrote a lot about it. They wanted people to know they could use this method when studying science. We know so many things today because scientists proved them with the scientific method. For example, how would we know about gravity if Isaac Newton didn’t drop an apple and a feather?

Simple Experiments to Try at Home

There are simple ways to carry out experiments in your house. Here are some of them.

Soda and Vinegar

For this experiment, you can pour soda and vinegar into a glass. Put some resins inside the glass. Watch how the resins move fast. Why are they moving like this?

Glitter and Soap

Fill up a tray with water. Squeeze some dish soap into the tray. Now pour glitter into the same try. Does the soap make the glitter float? If it does, then how is it that soap can help remove glitter from surfaces?

Draw a stick figure on a tray. Use an erasable board marker to draw the figure. Now fill the tray with water. Notice how the figure floats. Why does this happen? What does it prove about how easily erasable dry markers can be peeled away.

This is a simple experiment. You may have crushed many soda cans before throwing them in the trash. Have you ever wondered why empty soda cans can easily be crushed? What if you could destroy the can without squeezing it with your hands? Try placing the soda can in the water. Water puts a lot of pressure on the objects inside it. Observe how the soda can behave now.

Chalk from Eggshells

Did you know that you can make your chalk? This is because chalk and eggshells are made from the same material. Add food coloring to crushed shells and try drawing with them. What did you learn from this observation?

Why Is It Important?

It is essential for kids to understand the scientific method. It is where all the discoveries of science come from. It is also the accepted method for scientists and researchers to conduct research and solve issues. It is also useful because it helps us see different patterns in our surroundings and figure out why things happen.

Once you learn about the scientific method, you can easily prove any theory you have. If you think that more than 10 bees like to come near flowers in a day, you can watch and count the number of bees that come near a sunflower in your garden. If they are 10, then you’ll know that your theory is right.

What Are the 7 Steps of the Scientific Method?

Scientists and researchers use the scientific method to establish facts through experimentation and testing objectively. The scientific methods involve making observations, forming a hypothesis, making predictions, conducting experiments, and analyzing.

There are seven steps in the scientific method. Let us look at each of these steps in detail, but first, it is essential to understand what the scientific method is and why it is so crucial in research. Read on to find out!

What Is It and Why Is It So Important?

What makes the scientific methods so important is that it aids in the process of experimentation by providing an objective and standardized approach to it. Hence, this scientific method ultimately improves the quality of the experiments and enhances the accuracy of the results.

The scientific method ensures that the scientists or researchers are not influenced by personal or preconceived notions that can impact the study results, causing bias and inaccuracy. Using a standardized approach helps people stick to the facts and reduces their reliance on opinions.

The scientific method teaches you to assess and carefully go over all the evidence before making a statement, which is vital in science. It also trains the brain to examine and process information logically. It teaches one to be more observant, test all the facts, and make relevant connections and inferences.

The benefits of the scientific method go beyond science and research.

The Seven Steps -  Here are the seven steps of the scientific method that you should know about:

1. Ask a Question

The first step the defining and asking the question you want an answer to. You must ensure that your question is measurable in terms of experimentation. For example, it is quite likely for most results to be measured in numerical terms. Although it is relatively more challenging to measure behavioral results, they are also a part of the scientific method.

The question you ask could start with How, What, When, Who, Which, Why, or Where?

For example, if you want to carry out an experiment about the relationship between technology and student grades and performance, your question could be as follows:

Does technology directly or indirectly impact student performance in terms of academics?

This is an example of the research question, and the following steps will work toward finding an accurate answer to this question.

2. Perform Background Research

Conducting research is one of the most critical steps of the scientific method. Once you have formulated the research question, you need to conduct preliminary background research to understand what has been said previously about the topics.

Preliminary research will help you solidify your research topics by narrowing down your study or broadening it. At this point, you may want to narrow down your search. So, instead of assessing the impact of technology on student performance, you may want to base your study on the effects of mobile phones on student performance or student grades.

Depending on the type of research question, you can find relevant information in the following sources:

- Library resources - Internet - Books and magazines - Research journals - The newspaper - Biographies - Political commentary - Textbooks.

Taking the same example mentioned in the first step, you can review past scientific studies on the impact of mobile phones on students or teenagers.

3. Form or Propose a Hypothesis

The third step of the scientific method is forming a hypothesis. This step involves making an educated guess about how things work. In simpler words, to form a hypothesis means answering the research question in an explanatory manner that can be tested.

In the hypothesis statement, state your hypothesis and the prediction that you will be testing in your research. Keep in mind that your predictions must be easy to measure.

Here is an example of a hypothesis statement:

"If students use their phones excessively, then the students' grades are likely to fall."

4. Conduct an Experiment to Test Your Hypothesis

Now that you have formed your hypothesis statement, it is time to test whether your prediction is accurate. To test your hypothesis, you need to focus on facts and steer clear of your personal opinion and judgments to ensure the accuracy of the test results.

Conducting a fair test involves changing one factor at a time while all other factors remain constant.

Experimentation is an essential part of the scientific method as it is a way to test your predictions quantifiably.

For example, you can study the grades of students who own a cell phone and spend a lot of time on it, or you could look at the grades of students who own a cell phone but don't spend long hours on it.

Another approach could be to look at students' grades who don't own a cell phone. You must also factor in all the information you have gathered through other sources and focus on the relevant facts to your research.

5. Make Relevant Observations

In this step, you must assess your scientific process to ensure that all the conditions remain constant across all measures of experimentation. If you change factors in your experiment, you must keep all other factors constant to maintain fairness.

Once you have completed your experiment, it would be a good idea to run it a few more times to ensure the accuracy of the results.

6. Analyze the Results and Draw Conclusion

You've done all the hard work, and it is now time to assess the findings of your experiments and establish whether or not they support the hypothesis you formed. The process of drawing conclusions means determining whether what you believed to be true actually happened.

7. Present Your Findings

The last step is to compile and communicate the results of your study. Here are some of the forms you can use to present your findings:

- A presentation - A report - A journal

The benefits of the scientific method go beyond science and research and are particularly important for students. We hope this guide was helpful in understanding the seven steps of the scientific method and will come in handy during your next study.

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1.3: Hypothesis, Theories, and Laws

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  Learning Objectives

• Describe the difference between hypothesis and theory as scientific terms.
• Describe the difference between a theory and scientific law.

Although many have taken science classes throughout the course of their studies, people often have incorrect or misleading ideas about some of the most important and basic principles in science. Most students have heard of hypotheses, theories, and laws, but what do these terms really mean? Prior to reading this section, consider what you have learned about these terms before. What do these terms mean to you? What do you read that contradicts or supports what you thought?

What is a Fact?

A fact is a basic statement established by experiment or observation. All facts are true under the specific conditions of the observation.

What is a Hypothesis?

One of the most common terms used in science classes is a "hypothesis". The word can have many different definitions, depending on the context in which it is being used:

• An educated guess: a scientific hypothesis provides a suggested solution based on evidence.
• Prediction: if you have ever carried out a science experiment, you probably made this type of hypothesis when you predicted the outcome of your experiment.
• Tentative or proposed explanation: hypotheses can be suggestions about why something is observed. In order for it to be scientific, however, a scientist must be able to test the explanation to see if it works and if it is able to correctly predict what will happen in a situation. For example, "if my hypothesis is correct, we should see ___ result when we perform ___ test."

A hypothesis is very tentative; it can be easily changed.

What is a Theory?

The United States National Academy of Sciences describes what a theory is as follows:

"Some scientific explanations are so well established that no new evidence is likely to alter them. The explanation becomes a scientific theory. In everyday language a theory means a hunch or speculation. Not so in science. In science, the word theory refers to a comprehensive explanation of an important feature of nature supported by facts gathered over time. Theories also allow scientists to make predictions about as yet unobserved phenomena."

"A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experimentation. Such fact-supported theories are not "guesses" but reliable accounts of the real world. The theory of biological evolution is more than "just a theory." It is as factual an explanation of the universe as the atomic theory of matter (stating that everything is made of atoms) or the germ theory of disease (which states that many diseases are caused by germs). Our understanding of gravity is still a work in progress. But the phenomenon of gravity, like evolution, is an accepted fact.

Note some key features of theories that are important to understand from this description:

• Theories are explanations of natural phenomena. They aren't predictions (although we may use theories to make predictions). They are explanations as to why we observe something.
• Theories aren't likely to change. They have a large amount of support and are able to satisfactorily explain numerous observations. Theories can, indeed, be facts. Theories can change, but it is a long and difficult process. In order for a theory to change, there must be many observations or pieces of evidence that the theory cannot explain.
• Theories are not guesses. The phrase "just a theory" has no room in science. To be a scientific theory carries a lot of weight; it is not just one person's idea about something

Theories aren't likely to change.

What is a Law?

Scientific laws are similar to scientific theories in that they are principles that can be used to predict the behavior of the natural world. Both scientific laws and scientific theories are typically well-supported by observations and/or experimental evidence. Usually scientific laws refer to rules for how nature will behave under certain conditions, frequently written as an equation. Scientific theories are more overarching explanations of how nature works and why it exhibits certain characteristics. As a comparison, theories explain why we observe what we do and laws describe what happens.

For example, around the year 1800, Jacques Charles and other scientists were working with gases to, among other reasons, improve the design of the hot air balloon. These scientists found, after many, many tests, that certain patterns existed in the observations on gas behavior. If the temperature of the gas is increased, the volume of the gas increased. This is known as a natural law. A law is a relationship that exists between variables in a group of data. Laws describe the patterns we see in large amounts of data, but do not describe why the patterns exist.

What is a Belief?

A belief is a statement that is not scientifically provable. Beliefs may or may not be incorrect; they just are outside the realm of science to explore.

Laws vs. Theories

A common misconception is that scientific theories are rudimentary ideas that will eventually graduate into scientific laws when enough data and evidence has accumulated. A theory does not change into a scientific law with the accumulation of new or better evidence. Remember, theories are explanations and laws are patterns we see in large amounts of data, frequently written as an equation. A theory will always remain a theory; a law will always remain a law.

Video \(\PageIndex{1}\): What’s the difference between a scientific law and theory?

• A hypothesis is a tentative explanation that can be tested by further investigation.
• A theory is a well-supported explanation of observations.
• A scientific law is a statement that summarizes the relationship between variables.
• An experiment is a controlled method of testing a hypothesis.

Contributions & Attributions

Marisa Alviar-Agnew  ( Sacramento City College )

Henry Agnew (UC Davis)

Scientific Laws and Theories

Scientific Laws and Theories teaches students about the differences between a law and a theory when it comes to science. Students will also learn how to differentiate among facts, beliefs, and hypotheses. They will be able to give examples of each of these five concepts.

There are additional suggestions in the “Options for Lesson” section of the classroom procedure page that you could incorporate into the lesson plan. For example, one idea is to divide students into five groups and assign each group one of the five concepts from the lesson to research further.

Description

Additional information, what our scientific laws and theories lesson plan includes.

Lesson Objectives and Overview: Scientific Laws and Theories introduces students to difference between a law and a theory in relation to the field of science. Students will discover what a fact is, what a hypothesis is, and what a belief is. They will learn how to differentiate among these five concepts and give examples of each. This lesson is for students in 5th grade and 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the yellow box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

You can check out the “Options for Lesson” section of the classroom procedure page for additional suggestions for ideas and activities to incorporate into the lesson. For the activity, students could work alone or in groups instead of in pairs. In addition, you could add a second or third scenario. Another option is to haves students create posters that show the differences among each of the scientific terms. You could also divide students into five groups, assign each group a term, and have the students research it further and find more examples. Another suggestion is to invite a scientist to the class to speak with students and answer their questions. One more options is to use current science content and have students identify facts, beliefs, theories, hypotheses, and laws from the content.

Teacher Notes

The teacher notes page provides an extra paragraph of information to help guide the lesson. It suggests teaching this lesson in conjunction with others that relate to the scientific method, processing skills, and so on. You can use the blank lines to write down any other ideas or thoughts you have about the topic as you prepare.

SCIENTIFIC LAWS AND THEORIES LESSON PLAN CONTENT PAGES

Laws, theories, facts, and more.

The Scientific Laws and Theories lesson plan contains four pages of content. Science concepts can often be quite simple or extremely difficult to understand. Students have probably learned many science-related concepts and ideas, such as the three main states of matter. They might understand that there are three states and be able to identify examples of each. But they may not understand why some matter can turn into a solid or why other substances can never turn into a liquid or gas.

There are a lot of scientific concepts, and we can’t label them all the same way. Scientists label their ideas as facts, theories, hypotheses, laws, or beliefs, depending on the traits or qualities of the idea. All these terms carry a different meaning in the field of science, and all scientists need to understand them.

Facts, Laws, and Hypotheses

The lesson provides a chart that explains each of the five labels. First, students will learn what a fact is in the field of science. Facts are basic statements that scientists have proven to be true through experiments and observation. If we observe rain from the sky, it is a fact that it’s raining. All facts are true under specific conditions, but in science, they may later be proven false when retested using better instruments or more thorough observation.

A law is a logical relationship between two or more things based on a variety of facts and proven hypotheses. Laws are often shown using mathematical formulas or statements of how two or more quantities relate to each other. Newton’s law of gravity, for example, predicts the behavior of a dropped object but does not explain why the object drops.

In science class, students often start an experiment with a hypothesis, an educated guess about what will happen and what they might observe. A hypothesis is a prediction of cause and effect. Additional experimentation and observation will either support or disprove a hypothesis. For instance, we might guess that all cleaning products are the same. After testing this idea out, we learn that some products are actually better than others, proving our hypothesis false.

Theories and Beliefs

A theory is the “why” in science. Theories explain why certain laws and facts exist, and we can test theories to determine their accuracy. Repeated testing can support a theory, and that theory will remain valid if there is no evidence to dispute it. Many times, we can label a theory as an accepted hypothesis.

One example of a theory is the idea that a large crater on Earth might have been caused by a meteor strike. However, this idea is not a proven fact, but many accept it to be true based on collected evidence. On the other hand, it’s possible that we can disprove the theory and find it to be false.

Finally, students will learn about beliefs. In science, a belief is a statement that is not scientifically provable in the same way as facts, laws, hypotheses, and theories. Beliefs that we proved to be false today can later be proven true by someone else using scientific experimenting and observation.

An example of a belief is the scenario in which many people believe there are certain lucky numbers, and the position of the planets affect how people behave. However, we cannot prove either of these beliefs to be true. It’s still possible that someone someday could change either of these beliefs into a fact after experimenting and observing.

Understanding the Difference

The difference between a theory, a law, a fact, and a hypothesis is subtle. Theories, laws, and facts often start out as as hypothesis when someone originally proposes it. After going through rigorous testing, experimentation, and observation, it’s possible that the hypothesis becomes one of the other three.

In addition, a fact may be true with certain conditions. For example, water boils at 212 °F at sea level, but at higher altitudes, it boils at lower temperatures. Every fact will depend on the specific circumstances under which a measurement is made. It is important to understand the differences.

How can you tell if a statement is a fact, law, hypothesis, theory, or belief? Facts are the statements that everyone knows to be true through direct observation. In science, we base facts on many lines of evidence. For example, at one time, it was a hypothesis that the planets circled the sun. With more observation and experimentation over time (and with better instruments), we learned that this was true, a fact. Newton discovered the law of gravity but could not explain why it worked. But others have explained it with a theory as to why it works. A theory will not become a law but explains the law.

The bottom of this page provides examples of each of the five categories of scientific concepts. Water freezes at 32°F, matter comprises atoms, and black holes exist. These are all facts. For every action, there is an equal and opposite reaction. Energy equals mass times the speed of light squared. Energy cannot be created or destroyed in a chemical reaction. These are all laws.

In the hypothesis group are three more statements. The sun will rise tomorrow morning. The universe was created at the big bang. Eating more vegetables will help a person lose weight. Theories include the idea that plate tectonics explain the movement of the continents. Natural selection explains the concept of evolution. Microorganisms cause many diseases.

Finally, humans were created separately from all other life on Earth. There are no such things as ghosts. The number 13 is unlucky, but the number 7 is lucky. These three statements all fall into the beliefs category.

SCIENTIFIC LAWS AND THEORIES LESSON PLAN WORKSHEETS

The Scientific Laws and Theories lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. Each one will reinforce students’ comprehension of lesson material in different ways and help them demonstrate when they learned. Use the guidelines on the classroom procedure page to determine when to distribute each worksheet to the class.

IMAGINATION ACTIVITY WORKSHEET

Students will work with a partner for the activity. The worksheet provides five separate prompts regarding different scenarios about astronauts visiting a new planet. Students will collaborate and share their ideas and thoughts with each other as they develop the answers for the prompts. The five prompts relate to either a hypothesis, fact, law, theory, or belief.

SCIENTIFIC LAWS AND THEORIES PRACTICE WORKSHEET

The practice worksheet divides into two sections. On the first section, students will match 15 explanations to the correct term. There is a word bank with five terms to choose from. Students will use each one three times. The second section requires students to decide whether each of five statements is true (T) or false (F).

FACT, THEORY, HYPOTHESIS, LAW, OR BELIEF HOMEWORK ASSIGNMENT

For the homework assignment, students will look at 20 statements. They must decide if the statement represents a fact (F), theory (T), hypothesis (H), law (L), or belief (B). The worksheet mentions that they can use the internet or other resources for help if necessary.

Worksheet Answer Keys

At the end of the lesson plan document are answer keys for the practice and homework worksheets. The correct answers are in red to make it easy to compare them to studnets’ work. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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9.E: Hypothesis Testing with One Sample (Exercises)

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These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

9.1: Introduction

9.2: null and alternative hypotheses.

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.

State the null hypothesis, \(H_{0}\), and the alternative hypothesis. \(H_{a}\), in terms of the appropriate parameter \((\mu \text{or} p)\).

• The mean number of years Americans work before retiring is 34.
• At most 60% of Americans vote in presidential elections.
• The mean starting salary for San Jose State University graduates is at least $100,000 per year.
• Twenty-nine percent of high school seniors get drunk each month.
• Fewer than 5% of adults ride the bus to work in Los Angeles.
• The mean number of cars a person owns in her lifetime is not more than ten.
• About half of Americans prefer to live away from cities, given the choice.
• Europeans have a mean paid vacation each year of six weeks.
• The chance of developing breast cancer is under 11% for women.
• Private universities' mean tuition cost is more than $20,000 per year.
• \(H_{0}: \mu = 34; H_{a}: \mu \neq 34\)
• \(H_{0}: p \leq 0.60; H_{a}: p > 0.60\)
• \(H_{0}: \mu \geq 100,000; H_{a}: \mu < 100,000\)
• \(H_{0}: p = 0.29; H_{a}: p \neq 0.29\)
• \(H_{0}: p = 0.05; H_{a}: p < 0.05\)
• \(H_{0}: \mu \leq 10; H_{a}: \mu > 10\)
• \(H_{0}: p = 0.50; H_{a}: p \neq 0.50\)
• \(H_{0}: \mu = 6; H_{a}: \mu \neq 6\)
• \(H_{0}: p ≥ 0.11; H_{a}: p < 0.11\)
• \(H_{0}: \mu \leq 20,000; H_{a}: \mu > 20,000\)

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is:

• \(p < 0.30\)
• \(p \leq 0.30\)
• \(p \geq 0.30\)
• \(p > 0.30\)

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:

• \(p = 0.20\)
• \(p > 0.20\)
• \(p < 0.20\)
• \(p \leq 0.20\)

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are:

• \(H_{0}: \bar{x} = 4.5, H_{a}: \bar{x} > 4.5\)
• \(H_{0}: \mu \geq 4.5, H_{a}: \mu < 4.5\)
• \(H_{0}: \mu = 4.75, H_{a}: \mu > 4.75\)
• \(H_{0}: \mu = 4.5, H_{a}: \mu > 4.5\)

9.3: Outcomes and the Type I and Type II Errors

State the Type I and Type II errors in complete sentences given the following statements.

• The mean number of cars a person owns in his or her lifetime is not more than ten.
• Private universities mean tuition cost is more than $20,000 per year.
• Type I error: We conclude that the mean is not 34 years, when it really is 34 years. Type II error: We conclude that the mean is 34 years, when in fact it really is not 34 years.
• Type I error: We conclude that more than 60% of Americans vote in presidential elections, when the actual percentage is at most 60%.Type II error: We conclude that at most 60% of Americans vote in presidential elections when, in fact, more than 60% do.
• Type I error: We conclude that the mean starting salary is less than $100,000, when it really is at least $100,000. Type II error: We conclude that the mean starting salary is at least $100,000 when, in fact, it is less than $100,000.
• Type I error: We conclude that the proportion of high school seniors who get drunk each month is not 29%, when it really is 29%. Type II error: We conclude that the proportion of high school seniors who get drunk each month is 29% when, in fact, it is not 29%.
• Type I error: We conclude that fewer than 5% of adults ride the bus to work in Los Angeles, when the percentage that do is really 5% or more. Type II error: We conclude that 5% or more adults ride the bus to work in Los Angeles when, in fact, fewer that 5% do.
• Type I error: We conclude that the mean number of cars a person owns in his or her lifetime is more than 10, when in reality it is not more than 10. Type II error: We conclude that the mean number of cars a person owns in his or her lifetime is not more than 10 when, in fact, it is more than 10.
• Type I error: We conclude that the proportion of Americans who prefer to live away from cities is not about half, though the actual proportion is about half. Type II error: We conclude that the proportion of Americans who prefer to live away from cities is half when, in fact, it is not half.
• Type I error: We conclude that the duration of paid vacations each year for Europeans is not six weeks, when in fact it is six weeks. Type II error: We conclude that the duration of paid vacations each year for Europeans is six weeks when, in fact, it is not.
• Type I error: We conclude that the proportion is less than 11%, when it is really at least 11%. Type II error: We conclude that the proportion of women who develop breast cancer is at least 11%, when in fact it is less than 11%.
• Type I error: We conclude that the average tuition cost at private universities is more than $20,000, though in reality it is at most $20,000. Type II error: We conclude that the average tuition cost at private universities is at most $20,000 when, in fact, it is more than $20,000.

For statements a-j in Exercise 9.109 , answer the following in complete sentences.

• State a consequence of committing a Type I error.
• State a consequence of committing a Type II error.

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is “the drug is unsafe.” What is the Type II Error?

• To conclude the drug is safe when in, fact, it is unsafe.
• Not to conclude the drug is safe when, in fact, it is safe.
• To conclude the drug is safe when, in fact, it is safe.
• Not to conclude the drug is unsafe when, in fact, it is unsafe.

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.

• at least 20%, when in fact, it is less than 20%.
• 20%, when in fact, it is 20%.
• less than 20%, when in fact, it is at least 20%.
• less than 20%, when in fact, it is less than 20%.

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average?

The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when, in fact, the mean number of hours

• is more than seven hours.
• is at most seven hours.
• is at least seven hours.
• is less than seven hours.

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:

• to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher
• to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
• to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
• to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

9.4: Distribution Needed for Hypothesis Testing

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average? The distribution to be used for this test is \(\bar{X} \sim\) ________________

• \(N\left(7.24, \frac{1.93}{\sqrt{22}}\right)\)
• \(N\left(7.24, 1.93\right)\)

9.5: Rare Events, the Sample, Decision and Conclusion

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

• Is this a test of one mean or proportion?
• State the null and alternative hypotheses. \(H_{0}\) : ____________________ \(H_{a}\) : ____________________
• Is this a right-tailed, left-tailed, or two-tailed test?
• What symbol represents the random variable for this test?
• In words, define the random variable for this test.
• \(x =\) ________________
• \(n =\) ________________
• \(p′ =\) _____________
• Calculate \(\sigma_{x} =\) __________. Show the formula set-up.
• State the distribution to use for the hypothesis test.
• Find the \(p\text{-value}\).
• Reason for the decision:
• Conclusion (write out in a complete sentence):

9.6: Additional Information and Full Hypothesis Test Examples

For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in [link] . Please feel free to make copies of the solution sheets. For the online version of the book, it is suggested that you copy the .doc or the .pdf files.

If you are using a Student's \(t\) - distribution for one of the following homework problems, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, however.)

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using \(\alpha = 0.05\), is the data highly inconsistent with the claim?

• \(H_{0}: \mu \geq 50,000\)
• \(H_{a}: \mu < 50,000\)
• Let \(\bar{X} =\) the average lifespan of a brand of tires.
• normal distribution
• \(z = -2.315\)
• \(p\text{-value} = 0.0103\)
• Check student’s solution.
• alpha: 0.05
• Decision: Reject the null hypothesis.
• Reason for decision: The \(p\text{-value}\) is less than 0.05.
• Conclusion: There is sufficient evidence to conclude that the mean lifespan of the tires is less than 50,000 miles.
• \((43,537, 49,463)\)

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a standard deviation of 20¢. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of 95¢ with a standard deviation of 18¢. Do the data support the claim at the 1% level?

• \(H_{0}: \mu = $1.00\)
• \(H_{a}: \mu \neq $1.00\)
• Let \(\bar{X} =\) the average cost of a daily newspaper.
• \(z = –0.866\)
• \(p\text{-value} = 0.3865\)
• \(\alpha: 0.01\)
• Decision: Do not reject the null hypothesis.
• Reason for decision: The \(p\text{-value}\) is greater than 0.01.
• Conclusion: There is sufficient evidence to support the claim that the mean cost of daily papers is $1. The mean cost could be $1.
• \(($0.84, $1.06)\)

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let \(x =\) the number of sick days they took for the past year. Should the personnel team believe that the mean number is ten?

• \(H_{0}: \mu = 10\)
• \(H_{a}: \mu \neq 10\)
• Let \(\bar{X}\) the mean number of sick days an employee takes per year.
• Student’s t -distribution
• \(t = –1.12\)
• \(p\text{-value} = 0.300\)
• \(\alpha: 0.05\)
• Reason for decision: The \(p\text{-value}\) is greater than 0.05.
• Conclusion: At the 5% significance level, there is insufficient evidence to conclude that the mean number of sick days is not ten.
• \((4.9443, 11.806)\)

In 1955, Life Magazine reported that the 25 year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 81 women were surveyed with the following results. The sample mean was 83; the sample standard deviation was ten. Does it appear that the mean work week has increased for women at the 5% level?

Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think?

• \(H_{0}: p \geq 0.6\)
• \(H_{a}: p < 0.6\)
• Let \(P′ =\) the proportion of students who feel more enriched as a result of taking Elementary Statistics.
• normal for a single proportion
• \(p\text{-value} = 0.1308\)
• Conclusion: There is insufficient evidence to conclude that less than 60 percent of her students feel more enriched.

The “plus-4s” confidence interval is \((0.411, 0.648)\)

A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is 107. The average brown trout’s I.Q. is 4. So why can’t man catch brown trout?” Suppose you believe that the brown trout’s mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief.

Refer to Exercise 9.119 . Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout’s mean I.Q. is not four.

• \(H_{0}: \mu = 4\)
• \(H_{a}: \mu \neq 4\)
• Let \(\bar{X}\) the average I.Q. of a set of brown trout.
• two-tailed Student's t-test
• \(t = 1.95\)
• \(p\text{-value} = 0.076\)
• Reason for decision: The \(p\text{-value}\) is greater than 0.05
• Conclusion: There is insufficient evidence to conclude that the average IQ of brown trout is not four.
• \((3.8865,5.9468)\)

According to an article in Newsweek , the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don’t believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7?

A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent’s survey, would you agree with the Newsweek poll? In complete sentences, also give three reasons why the two polls might give different results.

• \(H_{a}: p < 0.13\)
• Let \(P′ =\) the proportion of Americans who have seen or sensed angels
• –2.688
• \(p\text{-value} = 0.0036\)
• Reason for decision: The \(p\text{-value}\)e is less than 0.05.
• Conclusion: There is sufficient evidence to conclude that the percentage of Americans who have seen or sensed an angel is less than 13%.

The“plus-4s” confidence interval is (0.0022, 0.0978)

The mean work week for engineers in a start-up company is believed to be about 60 hours. A newly hired engineer hopes that it’s shorter. She asks ten engineering friends in start-ups for the lengths of their mean work weeks. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours?

Data (length of mean work week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.

Use the “Lap time” data for Lap 4 (see [link] ) to test the claim that Terri finishes Lap 4, on average, in less than 129 seconds. Use all twenty races given.

• \(H_{0}: \mu \geq 129\)
• \(H_{a}: \mu < 129\)
• Let \(\bar{X} =\) the average time in seconds that Terri finishes Lap 4.
• Student's t -distribution
• \(t = 1.209\)
• Conclusion: There is insufficient evidence to conclude that Terri’s mean lap time is less than 129 seconds.
• \((128.63, 130.37)\)

Use the “Initial Public Offering” data (see [link] ) to test the claim that the mean offer price was $18 per share. Do not use all the data. Use your random number generator to randomly survey 15 prices.

The following questions were written by past students. They are excellent problems!

"Asian Family Reunion," by Chau Nguyen

Every two years it comes around.

We all get together from different towns.

In my honest opinion,

It's not a typical family reunion.

Not forty, or fifty, or sixty,

But how about seventy companions!

The kids would play, scream, and shout

One minute they're happy, another they'll pout.

The teenagers would look, stare, and compare

From how they look to what they wear.

The men would chat about their business

That they make more, but never less.

Money is always their subject

And there's always talk of more new projects.

The women get tired from all of the chats

They head to the kitchen to set out the mats.

Some would sit and some would stand

Eating and talking with plates in their hands.

Then come the games and the songs

And suddenly, everyone gets along!

With all that laughter, it's sad to say

That it always ends in the same old way.

They hug and kiss and say "good-bye"

And then they all begin to cry!

I say that 60 percent shed their tears

But my mom counted 35 people this year.

She said that boys and men will always have their pride,

So we won't ever see them cry.

I myself don't think she's correct,

So could you please try this problem to see if you object?

• \(H_{0}: p = 0.60\)
• \(H_{a}: p < 0.60\)
• Let \(P′ =\) the proportion of family members who shed tears at a reunion.
• –1.71
• Reason for decision: \(p\text{-value} < \alpha\)
• Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the proportion of family members who shed tears at a reunion is less than 0.60. However, the test is weak because the \(p\text{-value}\) and alpha are quite close, so other tests should be done.
• We are 95% confident that between 38.29% and 61.71% of family members will shed tears at a family reunion. \((0.3829, 0.6171)\). The“plus-4s” confidence interval (see chapter 8) is \((0.3861, 0.6139)\)

Note that here the “large-sample” \(1 - \text{PropZTest}\) provides the approximate \(p\text{-value}\) of 0.0438. Whenever a \(p\text{-value}\) based on a normal approximation is close to the level of significance, the exact \(p\text{-value}\) based on binomial probabilities should be calculated whenever possible. This is beyond the scope of this course.

"The Problem with Angels," by Cyndy Dowling

Although this problem is wholly mine,

The catalyst came from the magazine, Time.

On the magazine cover I did find

The realm of angels tickling my mind.

Inside, 69% I found to be

In angels, Americans do believe.

Then, it was time to rise to the task,

Ninety-five high school and college students I did ask.

Viewing all as one group,

Random sampling to get the scoop.

So, I asked each to be true,

"Do you believe in angels?" Tell me, do!

Hypothesizing at the start,

Totally believing in my heart

That the proportion who said yes

Would be equal on this test.

Lo and behold, seventy-three did arrive,

Out of the sample of ninety-five.

Now your job has just begun,

Solve this problem and have some fun.

"Blowing Bubbles," by Sondra Prull

Studying stats just made me tense,

I had to find some sane defense.

Some light and lifting simple play

To float my math anxiety away.

Blowing bubbles lifts me high

Takes my troubles to the sky.

POIK! They're gone, with all my stress

Bubble therapy is the best.

The label said each time I blew

The average number of bubbles would be at least 22.

I blew and blew and this I found

From 64 blows, they all are round!

But the number of bubbles in 64 blows

Varied widely, this I know.

20 per blow became the mean

They deviated by 6, and not 16.

From counting bubbles, I sure did relax

But now I give to you your task.

Was 22 a reasonable guess?

Find the answer and pass this test!

• \(H_{0}: \mu \geq 22\)
• \(H_{a}: \mu < 22\)
• Let \(\bar{X} =\) the mean number of bubbles per blow.
• –2.667
• \(p\text{-value} = 0.00486\)
• Conclusion: There is sufficient evidence to conclude that the mean number of bubbles per blow is less than 22.
• \((18.501, 21.499)\)

"Dalmatian Darnation," by Kathy Sparling

A greedy dog breeder named Spreckles

Bred puppies with numerous freckles

The Dalmatians he sought

Possessed spot upon spot

The more spots, he thought, the more shekels.

His competitors did not agree

That freckles would increase the fee.

They said, “Spots are quite nice

But they don't affect price;

One should breed for improved pedigree.”

The breeders decided to prove

This strategy was a wrong move.

Breeding only for spots

Would wreak havoc, they thought.

His theory they want to disprove.

They proposed a contest to Spreckles

Comparing dog prices to freckles.

In records they looked up

One hundred one pups:

Dalmatians that fetched the most shekels.

They asked Mr. Spreckles to name

An average spot count he'd claim

To bring in big bucks.

Said Spreckles, “Well, shucks,

It's for one hundred one that I aim.”

Said an amateur statistician

Who wanted to help with this mission.

“Twenty-one for the sample

Standard deviation's ample:

They examined one hundred and one

Dalmatians that fetched a good sum.

They counted each spot,

Mark, freckle and dot

And tallied up every one.

Instead of one hundred one spots

They averaged ninety six dots

Can they muzzle Spreckles’

Obsession with freckles

Based on all the dog data they've got?

"Macaroni and Cheese, please!!" by Nedda Misherghi and Rachelle Hall

As a poor starving student I don't have much money to spend for even the bare necessities. So my favorite and main staple food is macaroni and cheese. It's high in taste and low in cost and nutritional value.

One day, as I sat down to determine the meaning of life, I got a serious craving for this, oh, so important, food of my life. So I went down the street to Greatway to get a box of macaroni and cheese, but it was SO expensive! $2.02 !!! Can you believe it? It made me stop and think. The world is changing fast. I had thought that the mean cost of a box (the normal size, not some super-gigantic-family-value-pack) was at most $1, but now I wasn't so sure. However, I was determined to find out. I went to 53 of the closest grocery stores and surveyed the prices of macaroni and cheese. Here are the data I wrote in my notebook:

Price per box of Mac and Cheese:

• 5 stores @ $2.02
• 15 stores @ $0.25
• 3 stores @ $1.29
• 6 stores @ $0.35
• 4 stores @ $2.27
• 7 stores @ $1.50
• 5 stores @ $1.89
• 8 stores @ 0.75.

I could see that the cost varied but I had to sit down to figure out whether or not I was right. If it does turn out that this mouth-watering dish is at most $1, then I'll throw a big cheesy party in our next statistics lab, with enough macaroni and cheese for just me. (After all, as a poor starving student I can't be expected to feed our class of animals!)

• \(H_{0}: \mu \leq 1\)
• \(H_{a}: \mu > 1\)
• Let \(\bar{X} =\) the mean cost in dollars of macaroni and cheese in a certain town.
• Student's \(t\)-distribution
• \(t = 0.340\)
• \(p\text{-value} = 0.36756\)
• Conclusion: The mean cost could be $1, or less. At the 5% significance level, there is insufficient evidence to conclude that the mean price of a box of macaroni and cheese is more than $1.
• \((0.8291, 1.241)\)

"William Shakespeare: The Tragedy of Hamlet, Prince of Denmark," by Jacqueline Ghodsi

THE CHARACTERS (in order of appearance):

• HAMLET, Prince of Denmark and student of Statistics
• POLONIUS, Hamlet’s tutor
• HOROTIO, friend to Hamlet and fellow student

Scene: The great library of the castle, in which Hamlet does his lessons

(The day is fair, but the face of Hamlet is clouded. He paces the large room. His tutor, Polonius, is reprimanding Hamlet regarding the latter’s recent experience. Horatio is seated at the large table at right stage.)

POLONIUS: My Lord, how cans’t thou admit that thou hast seen a ghost! It is but a figment of your imagination!

HAMLET: I beg to differ; I know of a certainty that five-and-seventy in one hundred of us, condemned to the whips and scorns of time as we are, have gazed upon a spirit of health, or goblin damn’d, be their intents wicked or charitable.

POLONIUS If thou doest insist upon thy wretched vision then let me invest your time; be true to thy work and speak to me through the reason of the null and alternate hypotheses. (He turns to Horatio.) Did not Hamlet himself say, “What piece of work is man, how noble in reason, how infinite in faculties? Then let not this foolishness persist. Go, Horatio, make a survey of three-and-sixty and discover what the true proportion be. For my part, I will never succumb to this fantasy, but deem man to be devoid of all reason should thy proposal of at least five-and-seventy in one hundred hold true.

HORATIO (to Hamlet): What should we do, my Lord?

HAMLET: Go to thy purpose, Horatio.

HORATIO: To what end, my Lord?

HAMLET: That you must teach me. But let me conjure you by the rights of our fellowship, by the consonance of our youth, but the obligation of our ever-preserved love, be even and direct with me, whether I am right or no.

(Horatio exits, followed by Polonius, leaving Hamlet to ponder alone.)

(The next day, Hamlet awaits anxiously the presence of his friend, Horatio. Polonius enters and places some books upon the table just a moment before Horatio enters.)

POLONIUS: So, Horatio, what is it thou didst reveal through thy deliberations?

HORATIO: In a random survey, for which purpose thou thyself sent me forth, I did discover that one-and-forty believe fervently that the spirits of the dead walk with us. Before my God, I might not this believe, without the sensible and true avouch of mine own eyes.

POLONIUS: Give thine own thoughts no tongue, Horatio. (Polonius turns to Hamlet.) But look to’t I charge you, my Lord. Come Horatio, let us go together, for this is not our test. (Horatio and Polonius leave together.)

HAMLET: To reject, or not reject, that is the question: whether ‘tis nobler in the mind to suffer the slings and arrows of outrageous statistics, or to take arms against a sea of data, and, by opposing, end them. (Hamlet resignedly attends to his task.)

(Curtain falls)

"Untitled," by Stephen Chen

I've often wondered how software is released and sold to the public. Ironically, I work for a company that sells products with known problems. Unfortunately, most of the problems are difficult to create, which makes them difficult to fix. I usually use the test program X, which tests the product, to try to create a specific problem. When the test program is run to make an error occur, the likelihood of generating an error is 1%.

So, armed with this knowledge, I wrote a new test program Y that will generate the same error that test program X creates, but more often. To find out if my test program is better than the original, so that I can convince the management that I'm right, I ran my test program to find out how often I can generate the same error. When I ran my test program 50 times, I generated the error twice. While this may not seem much better, I think that I can convince the management to use my test program instead of the original test program. Am I right?

• \(H_{0}: p = 0.01\)
• \(H_{a}: p > 0.01\)
• Let \(P′ =\) the proportion of errors generated
• Normal for a single proportion
• Decision: Reject the null hypothesis
• Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the proportion of errors generated is more than 0.01.

The“plus-4s” confidence interval is \((0.004, 0.144)\).

"Japanese Girls’ Names"

by Kumi Furuichi

It used to be very typical for Japanese girls’ names to end with “ko.” (The trend might have started around my grandmothers’ generation and its peak might have been around my mother’s generation.) “Ko” means “child” in Chinese characters. Parents would name their daughters with “ko” attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachiko—happy child, Yoshiko—a good child, Yasuko—a healthy child, and so on.

However, I noticed recently that only two out of nine of my Japanese girlfriends at this school have names which end with “ko.” More and more, parents seem to have become creative, modernized, and, sometimes, westernized in naming their children.

I have a feeling that, while 70 percent or more of my mother’s generation would have names with “ko” at the end, the proportion has dropped among my peers. I wrote down all my Japanese friends’, ex-classmates’, co-workers, and acquaintances’ names that I could remember. Following are the names. (Some are repeats.) Test to see if the proportion has dropped for this generation.

Ai, Akemi, Akiko, Ayumi, Chiaki, Chie, Eiko, Eri, Eriko, Fumiko, Harumi, Hitomi, Hiroko, Hiroko, Hidemi, Hisako, Hinako, Izumi, Izumi, Junko, Junko, Kana, Kanako, Kanayo, Kayo, Kayoko, Kazumi, Keiko, Keiko, Kei, Kumi, Kumiko, Kyoko, Kyoko, Madoka, Maho, Mai, Maiko, Maki, Miki, Miki, Mikiko, Mina, Minako, Miyako, Momoko, Nana, Naoko, Naoko, Naoko, Noriko, Rieko, Rika, Rika, Rumiko, Rei, Reiko, Reiko, Sachiko, Sachiko, Sachiyo, Saki, Sayaka, Sayoko, Sayuri, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yuki, Yuki, Yukiko, Yuko, Yuko.

"Phillip’s Wish," by Suzanne Osorio

My nephew likes to play

Chasing the girls makes his day.

He asked his mother

If it is okay

To get his ear pierced.

She said, “No way!”

To poke a hole through your ear,

Is not what I want for you, dear.

He argued his point quite well,

Says even my macho pal, Mel,

Has gotten this done.

It’s all just for fun.

C’mon please, mom, please, what the hell.

Again Phillip complained to his mother,

Saying half his friends (including their brothers)

Are piercing their ears

And they have no fears

He wants to be like the others.

She said, “I think it’s much less.

We must do a hypothesis test.

And if you are right,

I won’t put up a fight.

But, if not, then my case will rest.”

We proceeded to call fifty guys

To see whose prediction would fly.

Nineteen of the fifty

Said piercing was nifty

And earrings they’d occasionally buy.

Then there’s the other thirty-one,

Who said they’d never have this done.

So now this poem’s finished.

Will his hopes be diminished,

Or will my nephew have his fun?

• \(H_{0}: p = 0.50\)
• \(H_{a}: p < 0.50\)
• Let \(P′ =\) the proportion of friends that has a pierced ear.
• –1.70
• \(p\text{-value} = 0.0448\)
• Reason for decision: The \(p\text{-value}\) is less than 0.05. (However, they are very close.)
• Conclusion: There is sufficient evidence to support the claim that less than 50% of his friends have pierced ears.
• Confidence Interval: \((0.245, 0.515)\): The “plus-4s” confidence interval is \((0.259, 0.519)\).

"The Craven," by Mark Salangsang

Once upon a morning dreary

In stats class I was weak and weary.

Pondering over last night’s homework

Whose answers were now on the board

This I did and nothing more.

While I nodded nearly napping

Suddenly, there came a tapping.

As someone gently rapping,

Rapping my head as I snore.

Quoth the teacher, “Sleep no more.”

“In every class you fall asleep,”

The teacher said, his voice was deep.

“So a tally I’ve begun to keep

Of every class you nap and snore.

The percentage being forty-four.”

“My dear teacher I must confess,

While sleeping is what I do best.

The percentage, I think, must be less,

A percentage less than forty-four.”

This I said and nothing more.

“We’ll see,” he said and walked away,

And fifty classes from that day

He counted till the month of May

The classes in which I napped and snored.

The number he found was twenty-four.

At a significance level of 0.05,

Please tell me am I still alive?

Or did my grade just take a dive

Plunging down beneath the floor?

Upon thee I hereby implore.

Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

• \(H_{0}: p = 0.40\)
• \(H_{a}: p < 0.40\)
• Let \(P′ =\) the proportion of schoolmates who fear public speaking.
• –1.01
• \(p\text{-value} = 0.1563\)
• Conclusion: There is insufficient evidence to support the claim that less than 40% of students at the school fear public speaking.
• Confidence Interval: \((0.3241, 0.4240)\): The “plus-4s” confidence interval is \((0.3257, 0.4250)\).

Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. To test if 68% also represents California’s percent for full-time faculty teaching the online classes, Long Beach City College (LBCC) in California, was randomly selected for comparison. In the same year, 34 of the 44 online courses LBCC offered were taught by full-time faculty. Conduct a hypothesis test to determine if 68% represents California. NOTE: For more accurate results, use more California community colleges and this past year's data.

According to an article in Bloomberg Businessweek , New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year’s rate. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased.

• \(H_{0}: p = 0.14\)
• \(H_{a}: p < 0.14\)
• Let \(P′ =\) the proportion of NYC residents that smoke.
• –0.2756
• \(p\text{-value} = 0.3914\)
• At the 5% significance level, there is insufficient evidence to conclude that the proportion of NYC residents who smoke is less than 0.14.
• Confidence Interval: \((0.0502, 0.2070)\): The “plus-4s” confidence interval (see chapter 8) is \((0.0676, 0.2297)\).

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

Registered nurses earned an average annual salary of $69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was $71,121 with a sample standard deviation of $7,489. Conduct a hypothesis test.

• \(H_{0}: \mu = 69,110\)
• \(H_{0}: \mu > 69,110\)
• Let \(\bar{X} =\) the mean salary in dollars for California registered nurses.
• \(t = 1.719\)
• \(p\text{-value}: 0.0466\)
• Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the mean salary of California registered nurses exceeds $69,110.
• \(($68,757, $73,485)\)

La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old.

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

• Reject \(H_{0}\): There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
• Do not reject \(H_{0}\): There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.
• Do not reject \(H_{0}\): There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
• Reject \(H_{0}\): There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing.

At a 1% level of significance, an appropriate conclusion is:

• There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.
• There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is more than 20%.
• There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.
• There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is at least 20%.

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

At a significance level of \(a = 0.05\), what is the correct conclusion?

• There is enough evidence to conclude that the mean number of hours is more than 4.75
• There is enough evidence to conclude that the mean number of hours is more than 4.5
• There is not enough evidence to conclude that the mean number of hours is more than 4.5
• There is not enough evidence to conclude that the mean number of hours is more than 4.75

Instructions: For the following ten exercises,

Hypothesis testing: For the following ten exercises, answer each question.

State the null and alternate hypothesis.

State the \(p\text{-value}\).

State \(\alpha\).

What is your decision?

Write a conclusion.

Answer any other questions asked in the problem.

According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

• \(H_{0}: p = 0.488\) \(H_{a}: p \neq 0.488\)
• \(p\text{-value} = 0.0114\)
• \(\alpha = 0.05\)
• Reject the null hypothesis.
• At the 5% level of significance, there is enough evidence to conclude that 48.8% of families own stocks.
• The survey does not appear to be accurate.

Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. Using \(\alpha = 0.05\), is the AAA proportion accurate?

The US Department of Energy reported that 51.7% of homes were heated by natural gas. A random sample of 221 homes in Kentucky found that 115 were heated by natural gas. Does the evidence support the claim for Kentucky at the \(\alpha = 0.05\) level in Kentucky? Are the results applicable across the country? Why?

• \(H_{0}: p = 0.517\) \(H_{0}: p \neq 0.517\)
• \(p\text{-value} = 0.9203\).
• \(\alpha = 0.05\).
• Do not reject the null hypothesis.
• At the 5% significance level, there is not enough evidence to conclude that the proportion of homes in Kentucky that are heated by natural gas is 0.517.
• However, we cannot generalize this result to the entire nation. First, the sample’s population is only the state of Kentucky. Second, it is reasonable to assume that homes in the extreme north and south will have extreme high usage and low usage, respectively. We would need to expand our sample base to include these possibilities if we wanted to generalize this claim to the entire nation.

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use \(\alpha = 0.01\) level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the \(\alpha = 0.05 level\), can it be concluded that the mean rainfall was below the reported average? What if \(\alpha = 0.01\)? Assume the amount of summer rainfall follows a normal distribution.

• \(H_{0}: \mu \geq 11.52\) \(H_{a}: \mu < 11.52\)
• \(p\text{-value} = 0.000002\) which is almost 0.
• At the 5% significance level, there is enough evidence to conclude that the mean amount of summer rain in the northeaster US is less than 11.52 inches, on average.
• We would make the same conclusion if alpha was 1% because the \(p\text{-value}\) is almost 0.

A survey in the N.Y. Times Almanac finds the mean commute time (one way) is 25.4 minutes for the 15 largest US cities. The Austin, TX chamber of commerce feels that Austin’s commute time is less and wants to publicize this fact. The mean for 25 randomly selected commuters is 22.1 minutes with a standard deviation of 5.3 minutes. At the \(\alpha = 0.10\) level, is the Austin, TX commute significantly less than the mean commute time for the 15 largest US cities?

A report by the Gallup Poll found that a woman visits her doctor, on average, at most 5.8 times each year. A random sample of 20 women results in these yearly visit totals

3; 2; 1; 3; 7; 2; 9; 4; 6; 6; 8; 0; 5; 6; 4; 2; 1; 3; 4; 1

At the \(\alpha = 0.05\) level can it be concluded that the sample mean is higher than 5.8 visits per year?

• \(H_{0}: \mu \leq 5.8\) \(H_{a}: \mu > 5.8\)
• \(p\text{-value} = 0.9987\)
• At the 5% level of significance, there is not enough evidence to conclude that a woman visits her doctor, on average, more than 5.8 times a year.

According to the N.Y. Times Almanac the mean family size in the U.S. is 3.18. A sample of a college math class resulted in the following family sizes:

5; 4; 5; 4; 4; 3; 6; 4; 3; 3; 5; 5; 6; 3; 3; 2; 7; 4; 5; 2; 2; 2; 3; 2

At \(\alpha = 0.05\) level, is the class’ mean family size greater than the national average? Does the Almanac result remain valid? Why?

The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At α = 0.01 level, is the student academic group’s claim correct?

• \(H_{0}: \mu \geq 150\) \(H_{0}: \mu < 150\)
• \(p\text{-value} = 0.0622\)
• \(\alpha = 0.01\)
• At the 1% significance level, there is not enough evidence to conclude that freshmen students study less than 2.5 hours per day, on average.
• The student academic group’s claim appears to be correct.

9.7: Hypothesis Testing of a Single Mean and Single Proportion

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Writing a Hypothesis Worksheet & Answers

Subject: Primary science

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

29 October 2022

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*** Worksheet + Answers Set, made for teachers to just print & go!***

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*This activity was structured using teaching programs, ensuring its alignment to the Australian NSW NESA syllabus and learning outcomes. Such outcomes include SC4-8WS and SC4-9WS from the Stage 4 Science Syllabus.

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**Science Report Skills Worksheet Bundle + Answers Set!** Clear the confusion and misconceptions around writing scientific reports for students! The lessons include a teacher-guided component and an activity for students to practice their skills along with a sample answer set for teachers to print, teach and go! This bundle includes worksheets on writing- 1. Aim 2. Hypothesis 3. Materials & Risk Assessment 4. Variables 5. Method 6. Choosing the right graph 7. Assessing reliability, accuracy & validity 8. Bibliography For more awesome worksheets, check out the other items on my TES store! *This activity was structured using teaching programs, ensuring its alignment to the Australian NSW NESA syllabus and learning outcomes. Such outcomes include SC4-8WS and SC4-9WS from the Stage 4 Science Syllabus.

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Hypotheses Theories and Scientific Law

Today we will be comparing and contrasting Hypotheses, Theories, and Scientific Law.

Science is a way of making sense of the world around us. The theories and principles found in science as a discipline have been established through repeated and careful experimentation and observation . Scientific research is peer-reviewed by other specialists in the field to ensure that the findings are accurate and that the experiments used, and the findings are consistent and fair.

Scientific ideas can progress from a hypothesis, to a theory using testable, scientific laws. Only a few scientific facts are considered scientific laws and many hypotheses are tested to generate a theory .

A hypothesis (plural hypotheses) is an idea or suggestion that can be tested through observation or experimentation. On some occasions, a hypothesis may take the form of a question called an aim .

Hypotheses are often made after in depth background research or an inquiry has been conducted. Its purpose is to provide direction into further scientific research. Once a hypothesis has been made, it must be tested by conducting carefully designed and controlled experiment to prove it right or wrong .

The experiment must meet certain criteria so that the results are valid and reliable . Valid and reliable results come from experiments that:

• Change only one variable at a time.
• Control all other variables in the experiment.
• Use measuring instruments that give accurate results.
• Have repeated trials/tests to show consistent results.

This lesson from Khan Academy is also good. Here is the link...

Testing Hypothesis p-Values

A theory describes how or why something occurs. Scientists are always making new discoveries and so scientific theories evolve overtime.

In science a hypothesis or an idea is not considered a theory until it has been tested thoroughly and independently by many scientists. Scientific theories are more certain that hypotheses but less certain that scientific laws. Scientific theories are often made up of many hypotheses which add together to provide detailed information on a topic. In many cases, these theories have been contributed to by many scientists, often over several years.

A theory is:

• Consistent and compatible with the current scientific evidence available
• Tested against a wide range of phenomena
• Demonstrates effective problem-solving

Some of the more well-known theories that have contributed to modern biology and that are covered in this course are shown in the table below:

Here is a Hypotheses Theories and Scientific Law video to share with your class...

Scientific Laws

Theories which have been thoroughly tested and are accepted by the scientific community often become scientific laws. There are few laws compared to theories. Laws are often expressed as single statement and are brief but are concise.

Scientific Law vs Theory

This venn diagram show visually the difference between Scientific Law vs Theory.

Laws have the following features:

• They are universally accepted to be true.
• Laws predict the results under certain conditions.
• They do not provide explanations of how or why something occurs.

Below are examples of laws that will be covered in this course:

Here is a Scientific Law video to share with your class...

Here is your Free Content for this Lesson Hypotheses, Theories, and Scientific Law!

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Unit 1 – biology basics.

• 1-1  Nature of Science and the Scientific Method
• 1-2  Hypotheses, Theories and Scientific Law
• 1-3  Technological Design Process
• HS-LS1-6. Construct and revise an explanation based on evidence for how carbon, hydrogen and oxygen from sugar molecules may combine with other elements to form amino acids and/or other large carbon-based molecules.
• HS-ESS2-5. Plan and conduct an investigation of the properties of water and its effects on Earth materials and surface process.

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