use null hypothesis in a sentence

Statistics Made Easy

How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter <, >, ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)

Example 4: Burger Weights

A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

Published by Zach

Null Hypothesis Examples

The null hypothesis (H 0 ) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment .

The null hypothesis is the most powerful type of hypothesis in the scientific method because it’s the easiest one to test with a high confidence level using statistics. If the null hypothesis is accepted, then it’s evidence any observed differences between two experiment groups are due to random chance. If the null hypothesis is rejected, then it’s strong evidence there is a true difference between test sets or that the independent variable affects the dependent variable.

The null hypothesis is a nullifiable hypothesis. A researcher seeks to reject it because this result strongly indicates observed differences are real and not just due to chance.
The null hypothesis may be accepted or rejected, but not proven. There is always a level of confidence in the outcome.

What Is the Null Hypothesis?

The null hypothesis is written as H 0 , which is read as H-zero, H-nought, or H-null. It is associated with another hypothesis, called the alternate or alternative hypothesis H A or H 1 . When the null hypothesis and alternate hypothesis are written mathematically, they cover all possible outcomes of an experiment.

An experimenter tests the null hypothesis with a statistical analysis called a significance test. The significance test determines the likelihood that the results of the test are not due to chance. Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01). But, even if the confidence in the test is high, there is always a small chance the outcome is incorrect. This means you can’t prove a null hypothesis. It’s also a good reason why it’s important to repeat experiments.

Exact and Inexact Null Hypothesis

The most common type of null hypothesis assumes no difference between two samples or groups or no measurable effect of a treatment. This is the exact hypothesis . If you’re asked to state a null hypothesis for a science class, this is the one to write. It is the easiest type of hypothesis to test and is the only one accepted for certain types of analysis. Examples include:

There is no difference between two groups H 0 : μ 1 = μ 2 (where H 0 = the null hypothesis, μ 1 = the mean of population 1, and μ 2 = the mean of population 2)

Both groups have value of 100 (or any number or quality) H 0 : μ = 100

However, sometimes a researcher may test an inexact hypothesis . This type of hypothesis specifies ranges or intervals. Examples include:

Recovery time from a treatment is the same or worse than a placebo: H 0 : μ ≥ placebo time

There is a 5% or less difference between two groups: H 0 : 95 ≤ μ ≤ 105

An inexact hypothesis offers “directionality” about a phenomenon. For example, an exact hypothesis can indicate whether or not a treatment has an effect, while an inexact hypothesis can tell whether an effect is positive of negative. However, an inexact hypothesis may be harder to test and some scientists and statisticians disagree about whether it’s a true null hypothesis .

How to State the Null Hypothesis

To state the null hypothesis, first state what you expect the experiment to show. Then, rephrase the statement in a form that assumes there is no relationship between the variables or that a treatment has no effect.

Example: A researcher tests whether a new drug speeds recovery time from a certain disease. The average recovery time without treatment is 3 weeks.

State the goal of the experiment: “I hope the average recovery time with the new drug will be less than 3 weeks.”
Rephrase the hypothesis to assume the treatment has no effect: “If the drug doesn’t shorten recovery time, then the average time will be 3 weeks or longer.” Mathematically: H 0 : μ ≥ 3

This null hypothesis (inexact hypothesis) covers both the scenario in which the drug has no effect and the one in which the drugs makes the recovery time longer. The alternate hypothesis is that average recovery time will be less than three weeks:

H A : μ < 3

Of course, the researcher could test the no-effect hypothesis (exact null hypothesis): H 0 : μ = 3

The danger of testing this hypothesis is that rejecting it only implies the drug affected recovery time (not whether it made it better or worse). This is because the alternate hypothesis is:

H A : μ ≠ 3 (which includes μ <3 and μ >3)

Even though the no-effect null hypothesis yields less information, it’s used because it’s easier to test using statistics. Basically, testing whether something is unchanged/changed is easier than trying to quantify the nature of the change.

Remember, a researcher hopes to reject the null hypothesis because this supports the alternate hypothesis. Also, be sure the null and alternate hypothesis cover all outcomes. Finally, remember a simple true/false, equal/unequal, yes/no exact hypothesis is easier to test than a more complex inexact hypothesis.

Adèr, H. J.; Mellenbergh, G. J. & Hand, D. J. (2007). Advising on Research Methods: A Consultant’s Companion . Huizen, The Netherlands: Johannes van Kessel Publishing. ISBN 978-90-79418-01-5 .
Cox, D. R. (2006). Principles of Statistical Inference . Cambridge University Press. ISBN 978-0-521-68567-2 .
Everitt, Brian (1998). The Cambridge Dictionary of Statistics . Cambridge, UK New York: Cambridge University Press. ISBN 978-0521593465.
Weiss, Neil A. (1999). Introductory Statistics (5th ed.). ISBN 9780201598773.

Understanding a Hypothesis (Definition, Null, and Examples)

You come home exhausted and plop down on the couch. You don’t know why you are feeling so weary. You think about several possible reasons. Is it because you stayed up late last night? Is it because you skipped breakfast? Or is it because you had to take the stairs due to a power outage? Or is it because of all the above reasons?

What you are doing is hypothesizing about why you are feeling tired.

If you enjoy reading detective stories, you would have already come across a hypothesis. A good whodunit mystery confounds the reader with multiple hypotheses about who committed the crime.

What is a Hypothesis?

The term hypothesis is often used in a scientific context as a possible explanation for an occurrence.

The word originated from ancient Greek and means “putting under” indicating its early association with experimentation.

A hypothesis is:

An assumption that serves as a starting point for further research
A supposition made on the basis of insufficient evidence
A tentative and logical statement that can be tested for its authenticity
An idea that seeks to explain why a phenomenon takes place
A prediction about the outcome of a study according to known facts
A proposal about the possible relationship between two or more variables

A scientist testing a hypothesis is no different from a detective investigating a crime scene. Famous detectives such as Sherlock Holmes combine the evidence with their powers of prediction to identify the criminal from several potential suspects.

The scientist examines each hypothesis rigorously for any inconsistencies through experiments before it can receive the stamp of approval.

Scientists accept a hypothesis as a theory only after it has been validated several times in different conditions. This includes use of scientific methods and protocols involving observation and analysis of results.

A good hypothesis seeks to establish a causal relationship between two or more variables, primarily between the independent and the dependent variable.

Brushing your teeth at least twice in a day reduces the incidence of dental caries.

The independent variable or cause in the above example is the number of times you brush in a day. The dependent variable or effect is the incidence of dental caries or cavities.

A scientist or researcher tests a hypothesis by changing the independent variable and measuring its effect on the dependent variable.

A relationship between a single independent and dependent variable is known as a simple hypothesis.

The mathematical expression of this relationship is:

where x is the independent variable and Y is the dependent variable and
where x is the input and Y is the output or a function of x

So, brushing your teeth at least twice daily is an input and the reduction of dental caries is an output or a function of the action of brushing your teeth.

If there are multiple independent variables or in some cases more than a single dependent variable, the statement is a complex hypothesis.

Brushing your teeth at least twice a day and using dental floss reduces the incidence of cavities and periodontitis.

In the above example the two independent variables are brushing teeth and using dental floss. The dependent variables are reduction in cavities and periodontitis or gum infection. In this example the two independent variables are common for the two dependent variables.

The equation of a complex hypothesis can be written as:

Y = f(x 1 +x 2 +x 3 …)

Y 1 = f(z 1 +z 2 +z 3 …)

where z is a different set of independent variables for Y1 as the dependent variable

Developing a Hypothesis

A hypothesis is a frame of reference or a window through which you observe a phenomenon. The phenomenon is the dependent variable. Your job is to determine the independent variables that are causing the event.

Cultivate the habit of looking for patterns in anything that happens. Train your mind to think in terms of stimulus and reaction or cause and effect.

This will enable you to glean insights from the knowledge you gather. You will then be able to write a strong hypothesis that focuses on the variables that matter over the noise.

The six steps to developing a hypothesis are:

Ask a question
Preliminary research
Formulate the hypothesis
Refine the hypothesis
Phrase your hypothesis in three ways
Write a null hypothesis

Ask a Question

The first step is to write a research question.

To write an effective research question be as curious as possible. Start with asking yourself a ton of questions.

Begin with broad and open-ended questions before narrowing it down to more specific ones.

You can use the 5W1H method to get into the mode of writing a research question.

What took place?
When did it happen?
Where did it occur?
Why did it take place?
Who did it affect ?
How did it happen?

The research question needs to be clear, objective , well-defined and measurable.

Do people who take health supplements log in fewer sick days at work in a year than those who don’t?

After you have framed the right question you can make an educated guess to answer it. This answer will be your preliminary hypothesis. Your hypothesis will attempt to answer the research question with observable facts through various experiments.

Preliminary Research

You don’t have to start from scratch. You can draw from preexisting knowledge and well-established theories to discount fallacious premises at the outset.

Resources that you can refer to include case studies, research papers and theses published in academic or scientific journals. A thorough background research will help you to look at the research question from several angles.

Do keep an open mind or a blank slate to avoid falling in the trap of preconceived notions and prejudices. Your initial research should help you focus on the areas where you are most likely to find the answers.

You can come up with a blueprint or outline highlighting the variables that you think are most relevant to your research question.

Think how changing the attributes of a single variable potentially affects others. You may need to operationalize or define how you are going to measure the variables and their effects.

Formulate the Hypothesis

It’s time now to put together your hypothesis into words.

A sound hypothesis states:

Who or what is being studied?
The relationship between the variables
A measurable and reproducible outcome
The possibility to prove it as true or false

Teenagers in the 14-16 age group who eat a high-protein diet are taller by two inches than the average height for that age group.

The next step is to ensure your statement ticks all the boxes for a strong hypothesis.

Is the hypothesis:

Precise and quantifiable without any ambiguity
Lucid and focused on the results described in the research question

Does the hypothesis include:

An independent and dependent variable
Variables that can be changed or controlled
Terms that even a layman can understand
A well-defined outcome

Phrase your Hypothesis in Three Ways

A hypothesis is often written in an If-then format. This format describes the cause and effect relationship between an independent variable and a dependent variable.

Phrase your hypothesis as “If {you make changes to an independent variable} then {you will observe this change in the dependent variable}.”

If employees are given more autonomy to take work-related decisions then their overall performance improves.

Another way to write a hypothesis is by directly stating the outcome between the two variables.

More autonomy in terms of taking work-related decisions helps to improve an employee’s overall performance.

You can also state a hypothesis as a comparison between two groups.

Employees who are offered more autonomy to take work-related decisions show better overall performance than those who work in a micro-managed environment.

Write a Null Hypothesis

The next step is to frame a null hypothesis, especially if your study requires you to analyze the data statistically. A null hypothesis by default takes a converse position to the researcher’s hypothesis.

Your statement is known as the alternative hypothesis while its opposite outcome is referred to as the null hypothesis.

If you expect a change according to a relationship between the variables the null hypothesis denies the possibility of any change or association between the variables. If you expect the conditions to remain constant the null hypothesis states that change will take place.

The null hypothesis is referred to as H 0. Your hypothesis which is the alternative is written as H 1 or H a .

H 1 : A player who is more than two meters tall has a better chance of winning the National Basketball Association Most Valuable Player Award.

H 0 : The height of a player does not affect his prospects of winning the National Basketball Association Most Valuable Player Award.

Hypothesis Examples

Examples of research questions.

Which loop diuretic drug is more effective for treating heart failure?
Does attending online learning sessions help students to improve their exam scores?
Does talking on the phone while driving cause more accidents?
Does increasing the pressure affect the rate of reaction between gases?
Is a person more likely to be obese if she or he eats unhealthy foods at least four times in a week?

Examples of a Hypothesis

The clinical trial of the new drug Furosemide proved that it is better at treating heart failure than other loop diuretic drugs such as Bumetanide.
The students who attended online learning sessions had better exam scores than those who skipped the sessions.
Drivers who talk on the phone are likely to have an accident than those who don’t.
Increasing the pressure affects the concentration of gases and it acts as a catalyst in speeding up the rate of reaction.
People who eat processed foods frequently are more likely to be obese than people who limit their intake of such foods.

Examples of a Null Hypothesis

The clinical trial proved that there is no difference between the effectiveness of Furosemide and other loop diuretic drugs, such as Bumetanide, for treating heart failure.
There is no difference in the exam scores of students who attended online learning sessions and those who did not attend.
There is no difference in the rate of accidents experienced by drivers who talk on the phone compared with those who don’t talk on the phone while driving.
The elevation of pressure has no effect on the rate of reaction between gases.
The food consumed and its frequency of consumption do not affect the probability of a person becoming obese.

What are Null Hypotheses?

The null hypothesis states the opposite outcome to the researcher’s hypothesis.

In most cases, the null hypothesis’s default position is a prediction that no relationship exists between any two or more variables. The null hypothesis denies the possibility of a causal relationship existing between an assumed independent and dependent variable.

The symbol of the null hypothesis is H 0 .

The notion of a null hypothesis fulfills the requirement of the falsifiability of a hypothesis before it can be accepted as valid.

A null hypothesis is often written as a negative statement that posits that the original hypothesis is false. It either claims that the results obtained are due to chance or there is no evidence to prove any change.

Original Hypothesis: Use of nitrogen fertilizers helps plants grow faster as compared to use of phosphorus or potassium fertilizers.

Null Hypothesis (H 0 ): The fertilizer used has no bearing on the rate of plant growth

What are Alternative Hypotheses?

An alternative hypothesis states the researcher’s supposition of a causal relationship between any two or more variables. Alternative hypotheses are based upon an observable effect and seek to predict how changing an independent variable will affect the dependent variable.

An alternative hypothesis is symbolized as H 1 or H a . It’s often written together with a null hypothesis with the two statements existing as a dual pair of opposite assumptions. Only a single statement among two can be true.

Alternative hypotheses try to determine that the results are obtained due to significant changes related to the variables and not due to chance.

Research Question: Does washing hands thoroughly with soap before eating a meal reduce the rate of recurrence of respiratory ailments?

Alternative Hypothesis (H 1 ): Washing hands with soap before eating reduces the rate of recurrence of respiratory ailments by 30% compared with those who neglect hand hygiene.

Null Hypothesis (H 0 ): Washing hands with soap before eating has no effect on the rate of recurrence of respiratory ailments.

What is Hypothesis Testing?

After you have formulated a hypothesis, you need to choose a research and testing method.

Use a descriptive approach when experiments are difficult to conduct. A descriptive method incorporates case studies and surveys to collect data.

You can employ statistical tools such as a correlational study to measure the relationship between variables.

A correlational study calculates the probability of whether a linkage between two variables can be determined or do the changes occur purely due to chance. Do note that correlation is not equivalent to causality.

This method lets you arrive at a conclusion by generalizing the data obtained without performing any actual experiments. A hypothesis proved using this approach is known as a statistical hypothesis.

The other approach is the experimental method in which causal relationships are established between different variables through demonstrations. A working or empirical hypothesis often makes use of the experimental method to determine the relationships between the variables.

The steps for testing a hypothesis experimentally are:

Design of experiments
Collating data
Analysis of observable facts
Summarizing the conclusions
Validating the hypothesis as a theory

How to Write a Good Hypothesis

To find ideas for a hypothesis, you can look through discussion sections in academic and scientific journals or browse online publications. You will come across questions that can be investigated further.

Simple Steps

The steps to write a strong hypothesis are:

Choose your frame of reference or direction for determining the cause
Such an approach is known as a directional hypothesis
If you are unable to determine a starting point or the current theories are ambiguous and contradictory, you can choose a non-directional approach
This method involves stating the facts and observations randomly and then seeking to find a pattern
Identify the key variables
A variable is any attribute that can have measurable values such as temperature, time, or length
Tentatively label some variables as independent and some as dependent
State the relationship between the variables using clear and objective language
Operationalize or define how you will measure the variables for testability
Write the statement in the If-then format. You can also write it as a declarative sentence
Avoid jargon and use simple words that can be understood by a layman
Write a null hypothesis to satisfy the condition of falsifiability

If you watch television for more than three hours a day, then your ability to concentrate diminishes.

How to Write a Scientific Hypothesis

A good scientific hypothesis is:

Consistent: Use preexisting knowledge as a springboard for further research
Testable: Include words that are quantifiable or measurable
Concise: Cut down on verbose phrases and use precise words
Scalable: Formulate the statement in a universal context based on the variables
Promising: State unexplained occurrences as loose ends that can be investigated further

Simple steps

Record your observations and facts about the topic
Evaluate your statements for possible links to determine the cause and effect
Document all potential explanations to analyze further
Write the null hypothesis along with your own hypothesis
This satisfies the requisite condition for a valid hypothesis. It can either be confirmed or disproved

If you plant cotton in black soil, then the production is boosted by 20% as compared to the output from red soil.

How to write a Psychology Hypothesis

A psychology hypothesis often begins with how the environment or certain parameters within it influence or cause a specific behavior.

To write a sound psychology hypothesis:

Choose a topic that you are genuinely interested in
Do not ramble. Keep it short and simple
Use previous research and your own study to direct your vision
Ascertain and define the variables
You can write the hypothesis either as an If-then statement
Other alternatives are to write the hypothesis as a direct sentence or a comparative supposition

Use the following questions to guide your understanding of the topic.

Is your hypothesis based on a preexisting theory or your own research?
Can your hypothesis be tested for falsifiability?
What are the independent and dependent variables?

People who exercise regularly are less at risk from depression than people who lead a sedentary life.

What is and How to Write a Good Hypothesis in Research?
How to Write a Hypothesis in 6 Steps
Developing Hypothesis and Research Questions
Forming a Good Hypothesis for Scientific Research
6 Hypothesis Examples in Psychology
Correlational Research | When & How to Use
How to Write a Strong Hypothesis in 6 Simple Steps
How to Develop a Good Research Hypothesis
How To Develop a Hypothesis (With Elements, Types and Examples)
Definition of Hypothesis

Inside this article

Fact checked: Content is rigorously reviewed by a team of qualified and experienced fact checkers. Fact checkers review articles for factual accuracy, relevance, and timeliness. Learn more.

About the author

Dalia Y.: Dalia is an English Major and linguistics expert with an additional degree in Psychology. Dalia has featured articles on Forbes, Inc, Fast Company, Grammarly, and many more. She covers English, ESL, and all things grammar on GrammarBrain.

Core lessons

Abstract Noun
Accusative Case
Active Sentence
Alliteration
Adjective Clause
Adjective Phrase
Adverbial Clause
Appositive Phrase
Body Paragraph
Compound Adjective
Complex Sentence
Compound Words
Compound Predicate
Common Noun
Comparative Adjective
Comparative and Superlative
Compound Noun
Compound Subject
Compound Sentence
Copular Verb
Collective Noun
Colloquialism
Conciseness
Conditional
Concrete Noun
Conjunction
Conjugation
Conditional Sentence
Comma Splice
Correlative Conjunction
Coordinating Conjunction
Coordinate Adjective
Cumulative Adjective
Dative Case
Declarative Statement
Direct Object Pronoun
Direct Object
Dangling Modifier
Demonstrative Pronoun
Demonstrative Adjective
Direct Characterization
Definite Article
Doublespeak
Equivocation Fallacy
Future Perfect Progressive
Future Simple
Future Perfect Continuous
Future Perfect
First Conditional
Gerund Phrase
Genitive Case
Helping Verb
Irregular Adjective
Irregular Verb
Imperative Sentence
Indefinite Article
Intransitive Verb
Introductory Phrase
Indefinite Pronoun
Indirect Characterization
Interrogative Sentence
Intensive Pronoun
Inanimate Object
Indefinite Tense
Infinitive Phrase
Interjection
Intensifier
Indicative Mood
Juxtaposition
Linking Verb
Misplaced Modifier
Nominative Case
Noun Adjective
Object Pronoun
Object Complement
Order of Adjectives
Parallelism
Prepositional Phrase
Past Simple Tense
Past Continuous Tense
Past Perfect Tense
Past Progressive Tense
Present Simple Tense
Present Perfect Tense
Personal Pronoun
Personification
Persuasive Writing
Parallel Structure
Phrasal Verb
Predicate Adjective
Predicate Nominative
Phonetic Language
Plural Noun
Punctuation
Punctuation Marks
Preposition
Preposition of Place
Parts of Speech
Possessive Adjective
Possessive Determiner
Possessive Case
Possessive Noun
Proper Adjective
Proper Noun
Present Participle
Quotation Marks
Relative Pronoun
Reflexive Pronoun
Reciprocal Pronoun
Subordinating Conjunction
Simple Future Tense
Stative Verb
Subjunctive
Subject Complement
Subject of a Sentence
Sentence Variety
Second Conditional
Superlative Adjective
Slash Symbol
Topic Sentence
Types of Nouns
Types of Sentences
Uncountable Noun
Vowels and Consonants

Popular lessons

Stay awhile. Your weekly dose of grammar and English fun.

The world's best online resource for learning English. Understand words, phrases, slang terms, and all other variations of the English language.

Abbreviations
Editorial Policy

school Campus Bookshelves
menu_book Bookshelves
perm_media Learning Objects
login Login
how_to_reg Request Instructor Account
hub Instructor Commons
Download Page (PDF)
Download Full Book (PDF)
Periodic Table
Physics Constants
Scientific Calculator
Reference & Cite
Tools expand_more
Readability

selected template will load here

This action is not available.

9.1: Null and Alternative Hypotheses

Last updated
Save as PDF
Page ID 23459

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

$H_0$: The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

$H_a$: The alternative hypothesis: It is a claim about the population that is contradictory to $H_0$ and what we conclude when we reject $H_0$. This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject $H_0$" if the sample information favors the alternative hypothesis or "do not reject $H_0$" or "decline to reject $H_0$" if the sample information is insufficient to reject the null hypothesis.

$H_{0}$ always has a symbol with an equal in it. $H_{a}$ never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example $\PageIndex{1}$

$H_{0}$: No more than 30% of the registered voters in Santa Clara County voted in the primary election. $p \leq 30$
$H_{a}$: More than 30% of the registered voters in Santa Clara County voted in the primary election. $p > 30$

Exercise $\PageIndex{1}$

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

$H_{0}$: The drug reduces cholesterol by 25%. $p = 0.25$
$H_{a}$: The drug does not reduce cholesterol by 25%. $p \neq 0.25$

Example $\PageIndex{2}$

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

$H_{0}: \mu = 2.0$
$H_{a}: \mu \neq 2.0$

Exercise $\PageIndex{2}$

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol $(=, \neq, \geq, <, \leq, >)$ for the null and alternative hypotheses.

$H_{0}: \mu \_ 66$
$H_{a}: \mu \_ 66$
$H_{0}: \mu = 66$
$H_{a}: \mu \neq 66$

Example $\PageIndex{3}$

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

$H_{0}: \mu \geq 5$
$H_{a}: \mu < 5$

Exercise $\PageIndex{3}$

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

$H_{0}: \mu \_ 45$
$H_{a}: \mu \_ 45$
$H_{0}: \mu \geq 45$
$H_{a}: \mu < 45$

Example $\PageIndex{4}$

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

$H_{0}: p \leq 0.066$
$H_{a}: p > 0.066$

Exercise $\PageIndex{4}$

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol ($=, \neq, \geq, <, \leq, >$) for the null and alternative hypotheses.

$H_{0}: p \_ 0.40$
$H_{a}: p \_ 0.40$
$H_{0}: p = 0.40$
$H_{a}: p > 0.40$

COLLABORATIVE EXERCISE

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

Evaluate the null hypothesis , typically denoted with $H_{0}$. The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality $(=, \leq \text{or} \geq)$
Always write the alternative hypothesis , typically denoted with $H_{a}$ or $H_{1}$, using less than, greater than, or not equals symbols, i.e., $(\neq, >, \text{or} <)$.
If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

$H_{0}$ and $H_{a}$ are contradictory.

If $\alpha \leq p$-value, then do not reject $H_{0}$.
If$\alpha > p$-value, then reject $H_{0}$.

$\alpha$ is preconceived. Its value is set before the hypothesis test starts. The $p$-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .

9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

H 0 : μ __ 66
H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

H 0 : μ __ 45
H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

H 0 : p __ 0.40
H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

Authors: Barbara Illowsky, Susan Dean
Publisher/website: OpenStax
Book title: Statistics
Publication date: Mar 27, 2020
Location: Houston, Texas
Book URL: https://openstax.org/books/statistics/pages/1-introduction
Section URL: https://openstax.org/books/statistics/pages/9-1-null-and-alternative-hypotheses

© Jan 23, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Null Hypothesis Examples

ThoughtCo / Hilary Allison

Scientific Method
Chemical Laws
Periodic Table
Projects & Experiments
Biochemistry
Physical Chemistry
Medical Chemistry
Chemistry In Everyday Life
Famous Chemists
Activities for Kids
Abbreviations & Acronyms
Weather & Climate
Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
B.A., Physics and Mathematics, Hastings College

The null hypothesis —which assumes that there is no meaningful relationship between two variables—may be the most valuable hypothesis for the scientific method because it is the easiest to test using a statistical analysis. This means you can support your hypothesis with a high level of confidence. Testing the null hypothesis can tell you whether your results are due to the effect of manipulating the dependent variable or due to chance.

What Is the Null Hypothesis?

The null hypothesis states there is no relationship between the measured phenomenon (the dependent variable) and the independent variable . You do not need to believe that the null hypothesis is true to test it. On the contrary, you will likely suspect that there is a relationship between a set of variables. One way to prove that this is the case is to reject the null hypothesis. Rejecting a hypothesis does not mean an experiment was "bad" or that it didn't produce results. In fact, it is often one of the first steps toward further inquiry.

To distinguish it from other hypotheses, the null hypothesis is written as H 0 (which is read as “H-nought,” "H-null," or "H-zero"). A significance test is used to determine the likelihood that the results supporting the null hypothesis are not due to chance. A confidence level of 95 percent or 99 percent is common. Keep in mind, even if the confidence level is high, there is still a small chance the null hypothesis is not true, perhaps because the experimenter did not account for a critical factor or because of chance. This is one reason why it's important to repeat experiments.

Examples of the Null Hypothesis

To write a null hypothesis, first start by asking a question. Rephrase that question in a form that assumes no relationship between the variables. In other words, assume a treatment has no effect. Write your hypothesis in a way that reflects this.

What Is a Hypothesis? (Science)
What 'Fail to Reject' Means in a Hypothesis Test
What Are the Elements of a Good Hypothesis?
Scientific Method Vocabulary Terms
Null Hypothesis Definition and Examples
Definition of a Hypothesis
Six Steps of the Scientific Method
Understanding Simple vs Controlled Experiments
Hypothesis Test for the Difference of Two Population Proportions
What Is the Difference Between Alpha and P-Values?
Null Hypothesis and Alternative Hypothesis
What Are Examples of a Hypothesis?
Hypothesis Test Example
How to Conduct a Hypothesis Test
What Is a P-Value?
The Difference Between Type I and Type II Errors in Hypothesis Testing

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

Knowledge Base
Methodology
How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection.

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Prevent plagiarism, run a free check.

Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

The relevant variables
The specific group being studied
The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis is not just a guess. It should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations, and statistical analysis of data).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 9 April 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

Is this article helpful?

Shona McCombes

Other students also liked, operationalisation | a guide with examples, pros & cons, what is a conceptual framework | tips & examples, a quick guide to experimental design | 5 steps & examples.

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

Knowledge Base

Methodology

How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

An independent variable is something the researcher changes or controls.
A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Here's why students love Scribbr's proofreading services

Discover proofreading & editing

Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

The relevant variables
The specific group being studied
The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

Sampling methods
Simple random sampling
Stratified sampling
Cluster sampling
Likert scales
Reproducibility

Statistics

Null hypothesis
Statistical power
Probability distribution
Effect size
Poisson distribution

Research bias

Optimism bias
Cognitive bias
Implicit bias
Hawthorne effect
Anchoring bias
Explicit bias

Prevent plagiarism. Run a free check.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved April 9, 2024, from https://www.scribbr.com/methodology/hypothesis/

Is this article helpful?

Shona McCombes

Other students also liked, construct validity | definition, types, & examples, what is a conceptual framework | tips & examples, operationalization | a guide with examples, pros & cons, what is your plagiarism score.

School Guide
Mathematics
Number System and Arithmetic
Trigonometry
Probability
Mensuration
Maths Formulas
Class 8 Maths Notes
Class 9 Maths Notes
Class 10 Maths Notes
Class 11 Maths Notes
Class 12 Maths Notes
Greater Than and Less Than Symbols | Meaning of Signs and Examples
Numerator in Mathematics
Rational and Irrational Numbers
Expanded Form
Perfect Cubes - Definition, List, Chart and Examples
Linear Algebra Symbols
Divisibility Rule of 11
Perfect Numbers
Denominator in Maths
Additive Inverse and Multiplicative Inverse
Measurement
Predecessor and Successor
Binary Multiplication
Area and Perimeter of Shapes | Formula and Examples
Probability and Statistics
Number Symbols
Square Root of 4
Factors of 30
Binary Division

Null Hypothesis

Null Hypothesis , often denoted as H 0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is t he truth or falsity of an idea in analysis.

In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.

Table of Content

What Is a Null Hypothesis?

Symbol of Null Hypothesis

Formula of null hypothesis, types of null hypothesis, principle of null hypothesis, how do you find null hypothesis, what is a null hypothesis.

Null Hypothesis in statistical analysis suggests the absence of statistical significance within a specific set of observed data. Hypothesis testing, using sample data, evaluates the validity of this hypothesis. Commonly denoted as H 0 or simply “null,” it plays an important role in quantitative analysis, examining theories related to markets, investment strategies, or economies to determine their validity.

Definition of Null Hypothesis

Null Hypothesis represent a default position, often suggesting no effect or difference, against which researchers compare their experimental results. The Null Hypothesis, often denoted as H 0 , asserts a default assumption in statistical analysis. It posits no significant difference or effect, serving as a baseline for comparison in hypothesis testing.

Null Hypothesis is represented as H 0 , the Null Hypothesis symbolizes the absence of a measurable effect or difference in the variables under examination.

Certainly, a simple example would be asserting that the mean score of a group is equal to a specified value like stating that the average IQ of a population is 100.

The Null Hypothesis is typically formulated as a statement of equality or absence of a specific parameter in the population being studied. It provides a clear and testable prediction for comparison with the alternative hypothesis. The formulation of the Null Hypothesis typically follows a concise structure, stating the equality or absence of a specific parameter in the population.

Mean Comparison (Two-sample t-test)

H 0 : μ 1 = μ 2

This asserts that there is no significant difference between the means of two populations or groups.

Proportion Comparison

H 0 : p 1 − p 2 = 0

This suggests no significant difference in proportions between two populations or conditions.

Equality in Variance (F-test in ANOVA)

H 0 : σ 1 = σ 2

This states that there’s no significant difference in variances between groups or populations.

Independence (Chi-square Test of Independence):

H 0 : Variables are independent

This asserts that there’s no association or relationship between categorical variables.

Null Hypotheses vary including simple and composite forms, each tailored to the complexity of the research question. Understanding these types is pivotal for effective hypothesis testing.

Equality Null Hypothesis (Simple Null Hypothesis)

The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared.

Non-Inferiority Null Hypothesis

In some studies, the focus might be on demonstrating that a new treatment or method is not significantly worse than the standard or existing one.

Superiority Null Hypothesis

The concept of a superiority null hypothesis comes into play when a study aims to demonstrate that a new treatment, method, or intervention is significantly better than an existing or standard one.

Independence Null Hypothesis

In certain statistical tests, such as chi-square tests for independence, the null hypothesis assumes no association or independence between categorical variables.

Homogeneity Null Hypothesis

In tests like ANOVA (Analysis of Variance), the null hypothesis suggests that there’s no difference in population means across different groups.

Examples of Null Hypothesis

Medicine: Null Hypothesis: “No significant difference exists in blood pressure levels between patients given the experimental drug versus those given a placebo.”
Education: Null Hypothesis: “There’s no significant variation in test scores between students using a new teaching method and those using traditional teaching.”
Economics: Null Hypothesis: “There’s no significant change in consumer spending pre- and post-implementation of a new taxation policy.”
Environmental Science: Null Hypothesis: “There’s no substantial difference in pollution levels before and after a water treatment plant’s establishment.”

The principle of the null hypothesis is a fundamental concept in statistical hypothesis testing. It involves making an assumption about the population parameter or the absence of an effect or relationship between variables.

In essence, the null hypothesis (H 0 ) proposes that there is no significant difference, effect, or relationship between variables. It serves as a starting point or a default assumption that there is no real change, no effect or no difference between groups or conditions.

$\alpha$

Null Hypothesis Rejection

Rejecting the Null Hypothesis occurs when statistical evidence suggests a significant departure from the assumed baseline. It implies that there is enough evidence to support the alternative hypothesis, indicating a meaningful effect or difference. Null Hypothesis rejection occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Identifying the Null Hypothesis involves defining the status quotient, asserting no effect and formulating a statement suitable for statistical analysis.

When is Null Hypothesis Rejected?

The Null Hypothesis is rejected when statistical tests indicate a significant departure from the expected outcome, leading to the consideration of alternative hypotheses. It occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Null Hypothesis and Alternative Hypothesis

In the realm of hypothesis testing, the null hypothesis (H 0 ) and alternative hypothesis (H₁ or Ha) play critical roles. The null hypothesis generally assumes no difference, effect, or relationship between variables, suggesting that any observed change or effect is due to random chance. Its counterpart, the alternative hypothesis, asserts the presence of a significant difference, effect, or relationship between variables, challenging the null hypothesis. These hypotheses are formulated based on the research question and guide statistical analyses.

Null Hypothesis vs Alternative Hypothesis

The null hypothesis (H 0 ) serves as the baseline assumption in statistical testing, suggesting no significant effect, relationship, or difference within the data. It often proposes that any observed change or correlation is merely due to chance or random variation. Conversely, the alternative hypothesis (H 1 or Ha) contradicts the null hypothesis, positing the existence of a genuine effect, relationship or difference in the data. It represents the researcher’s intended focus, seeking to provide evidence against the null hypothesis and support for a specific outcome or theory. These hypotheses form the crux of hypothesis testing, guiding the assessment of data to draw conclusions about the population being studied.

Example of Alternative and Null Hypothesis

Let’s envision a scenario where a researcher aims to examine the impact of a new medication on reducing blood pressure among patients. In this context:

Null Hypothesis (H 0 ): “The new medication does not produce a significant effect in reducing blood pressure levels among patients.”

Alternative Hypothesis (H 1 or Ha): “The new medication yields a significant effect in reducing blood pressure levels among patients.”

The null hypothesis implies that any observed alterations in blood pressure subsequent to the medication’s administration are a result of random fluctuations rather than a consequence of the medication itself. Conversely, the alternative hypothesis contends that the medication does indeed generate a meaningful alteration in blood pressure levels, distinct from what might naturally occur or by random chance.

Also, Check

Solved Examples on Null Hypothesis

Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.

Null Hypothesis (H 0 ): The average time students spend on homework is equal to 2 hours per night. Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours. Test Statistic and Decision: Using a t-test, if the calculated t-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.

Example 2: A company asserts that the error rate in its production process is less than 1%.

Null Hypothesis (H 0 ): The error rate in the production process is 1% or higher. Data: A sample of 500 products shows an error rate of 0.8%. Test Statistic and Decision: Using a z-test, if the calculated z-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.

Null Hypothesis – Practice Problems

Q1. A researcher claims that the average time spent by students on homework is less than 2 hours per day. Formulate the null hypothesis for this claim?

Q2. A manufacturing company states that their new machine produces widgets with a defect rate of less than 5%. Write the null hypothesis to test this claim?

Q3. An educational institute believes that their online course completion rate is at least 60%. Develop the null hypothesis to validate this assertion?

Q4. A restaurant claims that the waiting time for customers during peak hours is not more than 15 minutes. Formulate the null hypothesis for this claim?

Q5. A study suggests that the mean weight loss after following a specific diet plan for a month is more than 8 pounds. Construct the null hypothesis to evaluate this statement?

Null Hypothesis – Frequently Asked Questions

How to form a null hypothesis.

A null hypothesis is formed based on the assumption that there is no significant difference or effect between the groups being compared or no association between variables being tested. It often involves stating that there is no relationship, no change, or no effect in the population being studied.

When Do we reject the Null Hypothesis?

In statistical hypothesis testing, if the p-value (the probability of obtaining the observed results) is lower than the chosen significance level (commonly 0.05), we reject the null hypothesis. This suggests that the data provides enough evidence to refute the assumption made in the null hypothesis.

What is a Null Hypothesis in Research?

In research, the null hypothesis represents the default assumption or position that there is no significant difference or effect. Researchers often try to test this hypothesis by collecting data and performing statistical analyses to see if the observed results contradict the assumption.

What Are Alternative and Null Hypotheses?

The null hypothesis (H0) is the default assumption that there is no significant difference or effect. The alternative hypothesis (H1 or Ha) is the opposite, suggesting there is a significant difference, effect or relationship.

What Does it Mean to Reject the Null Hypothesis?

Rejecting the null hypothesis implies that there is enough evidence in the data to support the alternative hypothesis. In simpler terms, it suggests that there might be a significant difference, effect or relationship between the groups or variables being studied.

How to Find Null Hypothesis?

Formulating a null hypothesis often involves considering the research question and assuming that no difference or effect exists. It should be a statement that can be tested through data collection and statistical analysis, typically stating no relationship or no change between variables or groups.

How is Null Hypothesis denoted?

The null hypothesis is commonly symbolized as H 0 in statistical notation.

What is the Purpose of the Null hypothesis in Statistical Analysis?

The null hypothesis serves as a starting point for hypothesis testing, enabling researchers to assess if there’s enough evidence to reject it in favor of an alternative hypothesis.

What happens if we Reject the Null hypothesis?

Rejecting the null hypothesis implies that there is sufficient evidence to support an alternative hypothesis, suggesting a significant effect or relationship between variables.

Is it Possible to Prove the Null Hypothesis?

No, statistical testing aims to either reject or fail to reject the null hypothesis based on evidence from sample data. It does not prove the null hypothesis to be true.

What are Test for Null Hypothesis?

Various statistical tests, such as t-tests or chi-square tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.

Please Login to comment...

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter , ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

Example 4: Burger Weights

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

How to Perform a Normality Test in Excel (Step-by-Step)

How to create a two way table in r (with examples), related posts, how to normalize data between -1 and 1, vba: how to check if string contains another..., how to interpret f-values in a two-way anova, how to create a vector of ones in..., how to determine if a probability distribution is..., what is a symmetric histogram (definition & examples), how to find the mode of a histogram..., how to find quartiles in even and odd..., how to calculate sxy in statistics (with example), how to calculate sxx in statistics (with example).

More from M-W
To save this word, you'll need to log in. Log In

null hypothesis

Definition of null hypothesis

Examples of null hypothesis in a sentence.

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'null hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

1935, in the meaning defined above

Dictionary Entries Near null hypothesis

Nullarbor Plain

Cite this Entry

“Null hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/null%20hypothesis. Accessed 11 Apr. 2024.

More from Merriam-Webster on null hypothesis

Britannica.com: Encyclopedia article about null hypothesis

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!

Play Quordle: Guess all four words in a limited number of tries. Each of your guesses must be a real 5-letter word.

Can you solve 4 words at once?

Word of the day.

See Definitions and Examples »

Get Word of the Day daily email!

Popular in Grammar & Usage

Your vs. you're: how to use them correctly, every letter is silent, sometimes: a-z list of examples, more commonly mispronounced words, how to use em dashes (—), en dashes (–) , and hyphens (-), absent letters that are heard anyway, popular in wordplay, the words of the week - apr. 5, 12 bird names that sound like compliments, 10 scrabble words without any vowels, 12 more bird names that sound like insults (and sometimes are), 8 uncommon words related to love, games & quizzes.

Play Blossom: Solve today's spelling word game by finding as many words as you can using just 7 letters. Longer words score more points.

About These Results

Advanced Search

Only registered users can use the advanced search. Signup for FREE now, or login if you already have an account.

Popular Phrases

stress ridden
get through
highly demanded
conscious of time

Hey, you should join our mailing list!

Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses.

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

H a : The alternative hypothesis : It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

After you have determined which hypothesis the sample supports, you make adecision. There are two options for a decision . They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p = 30

H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

H 0 : μ = 2.0

H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, <, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66

H 0 : μ = 66
H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ = 5

H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, <, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45

H 0 : μ = 45
H a : μ < 45

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

H 0 : p = 0.066

H a : p > 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, <, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40

H 0 : p = 0.40
H a : p > 0.40

Concept Review

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

H 0 and H a are contradictory.

OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

IMAGES

15 Null Hypothesis Examples (2024)
how to write a hypothesis generator
How to Write a Null Hypothesis (with Examples and Templates)
Top Notch How To Write A Research Hypothesis And Null Non Chronological
How to Write a Null Hypothesis (with Examples and Templates)
Null And Research Hypothesis Examples /

VIDEO

Null & Alternative Hypothesis |Statistical Hypothesis #hypothesis #samplingdistribution #statistics
Null hypothesis (H0) and Alternative hypothesis (H1)#SHORT
Null & Alternate Hypothesis and type 1& 2 error / Sanjay Routh
Null hypothesis/Tests of significance
Null Hypothesis and Alternative Hypothesis
Null Hypothesis

COMMENTS

Null & Alternative Hypotheses
Otherwise, you can use the general template sentences. General template sentences. The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:
Null Hypothesis: Definition, Rejecting & Examples
It is one of two mutually exclusive hypotheses about a population in a hypothesis test. When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H 0 or H A. Null Hypothesis H0: No effect exists in the population.
How to Write a Null Hypothesis (5 Examples)
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. HA (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign.
Null Hypothesis Definition and Examples
Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
Null Hypothesis Examples
An example of the null hypothesis is that light color has no effect on plant growth. The null hypothesis (H 0) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment.
Understanding a Hypothesis (Definition, Null, and Examples)
The null hypothesis denies the possibility of a causal relationship existing between an assumed independent and dependent variable. The symbol of the null hypothesis is H 0. The notion of a null hypothesis fulfills the requirement of the falsifiability of a hypothesis before it can be accepted as valid.
9.1: Null and Alternative Hypotheses
Review. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with $H_{0}$.The null is not rejected unless the hypothesis test shows otherwise.
Null and Alternative Hypotheses
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
9.1 Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
Examples of the Null Hypothesis
The null hypothesis—which assumes that there is no meaningful relationship between two variables—may be the most valuable hypothesis for the scientific method because it is the easiest to test using a statistical analysis. This means you can support your hypothesis with a high level of confidence. Testing the null hypothesis can tell you whether your results are due to the effect of ...
How to Write a Strong Hypothesis
Step 5: Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
How to Write a Strong Hypothesis
5. Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
Null hypothesis
The null hypothesis is what a researcher anticipates happening if the alternative hypothesis is not true. Therefore, in this case, the null hypothesis as a declarative sentence is. H 0: Average time for weight loss is either less than or equal to four weeks. This null hypothesis can be written mathematically as:
Null Hypothesis
Null Hypothesis, often denoted as H0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring.
Examples of "Null-hypothesis" in a Sentence
Null-hypothesis Sentence Examples. The null hypothesis is that not one of the available UFO reports represents a genuine sighting of an extraterrestrial spacecraft. Since t calc = 1.08 and t crit = 2.228, the null hypothesis is accepted. In this case, the correct decision is to reject the null hypothesis.
How to Write a Null Hypothesis (5 Examples)
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms: H0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. HA (Alternative Hypothesis): Population parameter , ≠ some value. Note that the null hypothesis always contains the equal sign.
Null hypotheses Definition & Meaning
The meaning of NULL HYPOTHESIS is a statistical hypothesis to be tested and accepted or rejected in favor of an alternative; specifically : the hypothesis that an observed difference (as between the means of two samples) is due to chance alone and not due to a systematic cause. ... Examples of null hypothesis in a Sentence.
null hypothesis in a sentence
Null is often used to represent unknown or undefined values. The null is a lifeless thing, an empty space. This is the process of creating a hypothesis based on observations and data, and then testing that hypothesis through experimentation. The evidence is strongly linked to the hypothesis.
Examples of "Null" in a Sentence
9. 4. Pope Nicholas declared orders given by Photius of Constantinople null. 4. 0. The cardinal number zero is the class of classes with no members; but there is only one such class, namely - the null class. 3. 0. The marriage of Alphonso and Urraca was declared null by the pope, as they were third cousins.
Null and Alternative Hypotheses
The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0: The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
Examples of "Hypothesis" in a Sentence
1. It follows that philosophy is in a sense both dualist and monist; it is a cosmic dualism inasmuch as it admits the possible existence of matter as a hypothesis, though it denies the possibility of any true knowledge of it, and is hence in regard of the only possible knowledge an idealistic monism. 1. 0.

How to Write a Null Hypothesis (5 Examples)

Example 1: Weight of Turtles

Example 2: Height of Males

Example 3: Graduation Rates

Example 4: Burger Weights

Example 5: Citizen Support

Additional Resources

Published by Zach

Null Hypothesis Examples

What Is the Null Hypothesis?

Exact and Inexact Null Hypothesis

How to State the Null Hypothesis

Related Posts

Understanding a Hypothesis (Definition, Null, and Examples)

A hypothesis is:

The mathematical expression of this relationship is:

The equation of a complex hypothesis can be written as:

The six steps to developing a hypothesis are:

Ask a Question

Preliminary Research

Formulate the Hypothesis

A sound hypothesis states:

Is the hypothesis:

Does the hypothesis include:

Phrase your Hypothesis in Three Ways

Write a Null Hypothesis

Hypothesis Examples

Examples of a Hypothesis

Examples of a Null Hypothesis

What are Null Hypotheses?

What are Alternative Hypotheses?

What is Hypothesis Testing?

The steps for testing a hypothesis experimentally are:

How to Write a Good Hypothesis

Simple Steps

How to Write a Scientific Hypothesis

Simple steps

How to write a Psychology Hypothesis

Core lessons

Popular lessons

Stay awhile. Your weekly dose of grammar and English fun.

9.1: Null and Alternative Hypotheses

Example \(\PageIndex{1}\)

Exercise \(\PageIndex{1}\)

Example \(\PageIndex{2}\)

Exercise \(\PageIndex{2}\)

Example \(\PageIndex{3}\)

Exercise \(\PageIndex{3}\)

Example \(\PageIndex{4}\)

Exercise \(\PageIndex{4}\)

COLLABORATIVE EXERCISE

Formula Review

9.1 Null and Alternative Hypotheses

Example 9.1

Example 9.2

Example 9.3

Example 9.4

Collaborative Exercise

Null Hypothesis Examples

What Is the Null Hypothesis?

Examples of the Null Hypothesis

Have a language expert improve your writing

How to Write a Strong Hypothesis | Guide & Examples

Table of contents

Variables in hypotheses

Prevent plagiarism, run a free check.

Step 2: Do some preliminary research

Step 3: Formulate your hypothesis

Step 4: Refine your hypothesis

Step 5: Phrase your hypothesis in three ways

Step 6. Write a null hypothesis

Cite this Scribbr article

Is this article helpful?

Shona McCombes

Have a language expert improve your writing

How to Write a Strong Hypothesis | Steps & Examples

Example: Hypothesis

Table of contents

Variables in hypotheses

Here's why students love Scribbr's proofreading services