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Chapter Questions

For the June temperature data in Table A.3: (a) Use a two-sample $t$ test to investigate whether the average June temperatures in El Niño and non-El Niño years are significantly different. Assume the Gaussian distribution is an adequate approximation to the distribution of the test statistic. (b) Construct a $95 \%$ confidence interval for the difference in average June temperature between El Niño and non-El Niño years.

Calculate $n^{\prime}$, the equivalent number of independent samples, for the two sets of minimum air temperature in Table A.1.

Use the data set in Table A.1 in Appendix A to test the null hypothesis that the average minimum temperatures for Ithaca and Canandaigua in January 1987 are equal. Compute $p$ values, assuming the Gaussian distribution is an adequate approximation to the null distribution of the test statistic, and (a) $H_{\mathrm{A}}=$ the minimum temperatures are different for the two locations. (b) $H_{\mathrm{A}}=$ the Canandaigua minimum temperatures are warmer.

Given that the correlations in Fig. 5.6a were computed using 29 years of data, use the Fisher 3 transformation to compute the magnitude of the correlation coefficient that was necessary for the null hypothesis to be rejected at the $5 \%$ level, versus the alternative that $r \neq 0$.

Test the fit of the Gaussian distribution to the July precipitation data in Table 4.5, using (a) A K-S test (b) A Chi-square $\left(\chi^2\right)$ test

Test whether the 1951-1980 July precipitation data in Table 4.5 could have been drawn from the same distribution as the 1951-1980 January precipitation comprising part of Table A.2, using the likelihood ratio test, assuming gamma distributions.

Use the Wilcoxon-Mann-Whitney test to investigate whether the magnitudes of the pressure data in Table A. 3 are lower in El Niño years: (a) Using the exact one-tailed critical values $18,14,11$, and 8 for tests at the $5 \%, 2.5 \%, 1 \%$, and $0.5 \%$ levels, respectively, for the smaller of $U_1$ and $U_2$. (b) Using the Gaussian approximation to the sampling distribution of $U$ (even though the sample size is too small for the approximation to be good).

Discuss how the sampling distribution of the skewness coefficient [Eq. (3.8)] of June precipitation at Guayaquil could be estimated using the data in Table A.3, by bootstrapping. How could the resulting bootstrap distribution be used to estimate a $95 \%$ confidence interval for this statistic? If the appropriate computing resources are available, implement your algorithm.

Discuss how to construct a resampling test to investigate whether the variance of June precipitation at Guayaquil is different in El Niño versus nonEl Niño years, using the data in Table A.3. If the appropriate computing resources are available, implement your algorithm.

A published article contains a statistical analysis of historical summer precipitation data in relation to summer temperatures using individual $t$ tests for 121 locations at the $10 \%$ level. The study investigates the null hypothesis of no difference in total precipitation between the 10 warmest summers in the period 1900-1969 and the remaining 60 summers, reports that 15 of the 121 tests exhibit significant results, and claims that the overall pattern is therefore significant. Evaluate this claim.

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• 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.

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 .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, 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 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 .

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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 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

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

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

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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.

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.

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McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved September 3, 2024, from https://www.scribbr.com/methodology/hypothesis/

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What Is a Testable Hypothesis?

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A hypothesis is a tentative answer to a scientific question. A testable hypothesis is a  hypothesis that can be proved or disproved as a result of testing, data collection, or experience. Only testable hypotheses can be used to conceive and perform an experiment using the scientific method .

Requirements for a Testable Hypothesis

In order to be considered testable, two criteria must be met:

• It must be possible to prove that the hypothesis is true.
• It must be possible to prove that the hypothesis is false.
• It must be possible to reproduce the results of the hypothesis.

Examples of a Testable Hypothesis

All the following hypotheses are testable. It's important, however, to note that while it's possible to say that the hypothesis is correct, much more research would be required to answer the question " why is this hypothesis correct?" 

• Students who attend class have higher grades than students who skip class.  This is testable because it is possible to compare the grades of students who do and do not skip class and then analyze the resulting data. Another person could conduct the same research and come up with the same results.
• People exposed to high levels of ultraviolet light have a higher incidence of cancer than the norm.  This is testable because it is possible to find a group of people who have been exposed to high levels of ultraviolet light and compare their cancer rates to the average.
• If you put people in a dark room, then they will be unable to tell when an infrared light turns on.  This hypothesis is testable because it is possible to put a group of people into a dark room, turn on an infrared light, and ask the people in the room whether or not an infrared light has been turned on.

Examples of a Hypothesis Not Written in a Testable Form

• It doesn't matter whether or not you skip class.  This hypothesis can't be tested because it doesn't make any actual claim regarding the outcome of skipping class. "It doesn't matter" doesn't have any specific meaning, so it can't be tested.
• Ultraviolet light could cause cancer.  The word "could" makes a hypothesis extremely difficult to test because it is very vague. There "could," for example, be UFOs watching us at every moment, even though it's impossible to prove that they are there!
• Goldfish make better pets than guinea pigs.  This is not a hypothesis; it's a matter of opinion. There is no agreed-upon definition of what a "better" pet is, so while it is possible to argue the point, there is no way to prove it.

How to Propose a Testable Hypothesis

Now that you know what a testable hypothesis is, here are tips for proposing one.

• Try to write the hypothesis as an if-then statement. If you take an action, then a certain outcome is expected.
• Identify the independent and dependent variable in the hypothesis. The independent variable is what you are controlling or changing. You measure the effect this has on the dependent variable.
• Write the hypothesis in such a way that you can prove or disprove it. For example, a person has skin cancer, you can't prove they got it from being out in the sun. However, you can demonstrate a relationship between exposure to ultraviolet light and increased risk of skin cancer.
• Make sure you are proposing a hypothesis you can test with reproducible results. If your face breaks out, you can't prove the breakout was caused by the french fries you had for dinner last night. However, you can measure whether or not eating french fries is associated with breaking out. It's a matter of gathering enough data to be able to reproduce results and draw a conclusion.
• What Are Examples of a Hypothesis?
• What Is a Hypothesis? (Science)
• What Are the Elements of a Good Hypothesis?
• Scientific Method Flow Chart
• Null Hypothesis Examples
• Scientific Hypothesis Examples
• Understanding Simple vs Controlled Experiments
• Six Steps of the Scientific Method
• Scientific Method Vocabulary Terms
• Scientific Variable
• What Is an Experimental Constant?
• What Is a Controlled Experiment?
• What Is the Difference Between a Control Variable and Control Group?
• DRY MIX Experiment Variables Acronym
• Random Error vs. Systematic Error
• The Role of a Controlled Variable in an Experiment

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• 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.

Table of contents

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.

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McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 3 September 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

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Enzymes ( CIE IGCSE Biology )

Topic questions.

Catalase is an enzyme found in plant and animal cells. It catalyses the breakdown of hydrogen peroxide to form water and oxygen.

The oxygen produced forms a foam. You can measure the height of the foam to determine catalase activity.

A student investigated catalase activity in cooked and uncooked potato tissue. 

The student: 

Fig. 1 shows the test-tubes after three minutes. 

Prepare a table to record your results.

Measure the height of the foam in each of the test-tubes in Fig. 1 Record these measurements in your table.

Calculate the difference in the height of the foam produced by the cooked and uncooked potato after three minutes.

State one conclusion for these results.

How did you do?

Identify the independent variable in this investigation. 

State why it is important that the two potato cylinders were identical in shape and size.

State two other variables that were kept constant in this investigation. 

Identify one possible source of error in the method used in this investigation. 

A student stated that:

'Catalase activity is the same in all species of plants'

Plan an investigation to test this statement.

Potatoes contain starch. Starch can be broken down into reducing sugars.

Describe the tests to identify starch and reducing sugars and give the results of the positive tests. 

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Some students investigated the activity of catalase.

Catalase is an enzyme found in plant and animal tissues. It catalyses the breakdown of hydrogen peroxide into water and oxygen. The activity of this enzyme can be measured by collecting the oxygen produced.  

2H 2 O 2                      →          2H 2 O     +     O 2 hydrogen peroxide                   water        oxygen       

The students used the apparatus shown in Fig. 1 to compare the activity of catalase using pieces of sweet potato of different sizes.  

Three cubes of 10 mm × 10 mm × 10 mm of sweet potato were used.

Cube 1 was placed into the test-tube and 5 cm 3 of hydrogen peroxide was added. The bung was quickly replaced into the top of the test-tube. The students carefully counted the number of bubbles of oxygen delivered into the water in one minute and then measured the final height of foam in the test-tube. For cube 1 , they counted 12 bubbles in one minute. The height of the foam was 42 mm. They then discarded the contents of the test-tube and rinsed it with clean water.

Cube 2 was cut into two pieces of approximately the same size. Both of these pieces were placed into the test-tube and 5 cm 3 of hydrogen peroxide was added as before. For cube 2 , they counted 23 bubbles in one minute. The height of foam was 63 mm. They then discarded the contents of the test-tube and rinsed it with clean water.

Cube 3 was cut into eight small pieces which were all placed into the test-tube and 5 cm 3 of hydrogen peroxide was added as before. For cube 3 , they counted 38 bubbles in one minute. The height of foam was 76 mm.

Prepare a table for the results from this investigation.

Use information provided in the question to complete your table.

State two variables that the students kept constant in this investigation.

Suggest how you could improve the method that they followed. 

State a conclusion that can be drawn from these results.

The students were given a hypothesis that said:

“The activity of catalase increases with increasing temperature”.

 Describe a similar investigation to the one carried out in a) to test this hypothesis.

Outline one safety precaution that you would need to take when performing this experiment.

Fruit juice can be produced by crushing and squeezing fresh fruit. The juice produced in this way is often cloudy.

The enzyme pectinase is used to produce clear fruit juice. This process is called clarification.

Fig. 1 shows fruit juice before and after clarification.

A student investigated the effect of pectinase concentration on the clarification of apple juice.

The student was provided with freshly prepared apple juice, water and a 5% pectinase solution.

Calculate the final concentration of the pectinase solution in test-tube P3 .

Show your king and write your answer to one decimal place.

Care was taken not to shake the test-tubes.

Fig.3 shows the test-tubes at 0, 5 and 10 minutes.

Note that the height of the precipitate is given for each test-tube.

Prepare a table to record the results.

State a conclusion for the results.

State the variable that was changed (independent variable) in this investigation.

State two variables that should have been kept constant in this investigation.

Identify one possible error in step 6 and suggest an improvement.

Explain the purpose of test-tube P4 .

A student stated the hypothesis: 

“Treating fruit juice with pectinase reduces the vitamin C content of the fruit juice”.

Plan an investigation to test this hypothesis. 

Fig. 4 shows a cross-section of a tomato fruit.

Make a large drawing of the cross-section of tomato fruit.

A student wanted to find out if tomatoes contained starch.

State the result you would expect for a positive test for starch.

Young mammals feed on milk containing protein.

Some mammals produce an enzyme called rennin. Rennin changes the protein in milk so that it can be digested by another enzyme.

The action of rennin causes small lumps or clots to form in the milk.

An investigation was carried out to find the effect of pH on the activity of the enzyme rennin.

Prepare a table in which to record these results. Use the information in Fig. 2 to complete this table.

State a conclusion for these results.

Suggest why, in step 8, all of the test-tubes were placed into a water-bath for three minutes before mixing the contents together in step 9.

State two variables that were kept constant in this investigation. 

Identify four sources of error in this investigation.

Identify one hazard associated with this procedure that would require the use of eye protection.

Clotting separates milk into a solid part and a liquid part.

Describe how you could find out if there was any protein remaining in the liquid part.

State the name of the test that would be used to test the milk for the presence of fat.

After rennin has changed the protein in milk into a white solid, protease enzymes can be used to digest the protein. The digested protein forms a colourless liquid.

A hypothesis stated:

The optimum temperature for protease enzymes to digest changed milk protein is 37°C.

Describe a method that could be used to test this hypothesis.