Academic Report Writing for Hypothesis Testing in Statistics

A report on a hypothesis test (e.g., Binomial test, one-sample t-test) should include:

• Introduction, including the alternative hypothesis for the study
• Sample description, together with quoting the sample size and any other appropriate

sample statistics

• Comparison of values (if looking at a difference in means or proportions)
• Comment on whether the observed difference (or relationship) is significant or not

significant, quoting appropriate statistics

• 95% confidence interval interpretation, quoting relevant values
• Conclusion which relates back to the alternative hypothesis

Note: sometimes the p-value will appear in SPSS output as .000. If that occurs, in a report it should be written as p < .001

We will look in more specific detail at report writing for one-sample t-tests and Binomial

tests below. But, in the later modules you will also see a similar general format as described

above, when writing reports for other types of hypothesis tests.

1. Report writing for one-sample t-tests

A report on a one-sample t-test should include:

• Introduction, including the alternative hypothesis for the study
• Sample description, including nature of the sample and mean, standard deviation and size of the sample

• Comparison of sample mean with reference mean
• Difference significant or not significant, quoting t, df and p
• 95% confidence interval interpretation, quoting relevant values
• Conclusion which relates back to the alternative hypothesis

Example 1

A university lecturer believes that the average amount of sleep per night for students taking

her unit differs from 8 hours per night. She took a random sample of her students and

asked each student how much sleep they typically have per night. Use the SPSS output

below to help write a report on the results of her study (testing at an alpha level of .05)

Report

A university lecturer hypothesised that the average amount of sleep per night for students

taking her unit differs from 8 hours per night.

For a random sample of 15 university students taking her unit, the average amount of sleep

per night was 7.20 hours (s = 0.86 hours). This is lower than 8 hours per night and a one-

sample t-test shows this difference in mean hours sleep per night is significant, t(14) =3.60,

p = .003

The 95% confidence interval shows that average hours sleep per night for university students taking the instructor’s unit is between 0.32 and 1.28 hours less than 8 hours.

As expected, the average amount of sleep per night for students taking the instructor’s unit differs from 8 hours, with her students on average sleeping less than 8 hours per night.

Example 2

In 2016, a report indicated that the average BMI of Australian adults was 27.44 kg per ².

Some health researchers believe the BMI of Australian adults has decreased since that time.

The following SPSS output was recently obtained for a random sample of Australian adults.

Is this data sufficient evidence to conclude that the BMI of Australian adults is lower than in

2016? Write a report on the results of this study.

Report

Health researchers hypothesised that the average BMI of Australian adults has decreased since 2016, when it was 27.44 kg per ².

For a random sample of 1716 Australian adults, the average BMI was 27.18 kg per 2

(s = 5.17 kg per ²). This is lower than the mean BMI of 27.44 recorded in 2016 and a one-

sample t-test shows this difference in mean BMI is significant, t(1715) =2.08, p = .038

The 95% confidence interval shows that average BMI of Australian adults is between 0.01

and 0.50 kg per ² lower than in 2016.

As expected, the average BMI of Australian adults has decreased since 2016.

Supplement_G_Report_Writing_One_Sample_ttest_&_Binomial_Test Page 3 of 5

1. Report writing for Binomial tests

A report on a Binomial test should include:

• Introduction, including the alternative hypothesis for the study
• Sample description, including nature of the sample, the sample proportion and the sample size

• Comparison of the sample proportion (or percentage) with the reference value • Difference significant or not significant, quoting n and p
• 95% confidence interval interpretation, quoting relevant values • Conclusion which relates back to the alternative hypothesis

Example 1

A newly established food company manufactures a cereal called Brekky Blockz. The

company claims that 30% of packets of Brekky Blockz contain a bonus novelty token.

However, some consumers suspect this claim is false - they believe that a lower

percentage of the Brekky Blockz packets contain the novelty token. The following

SPSS output was produced to investigate this (note that ‘packet contains a novelty

token?’ was coded 1 = yes, 2 = no).

Write a report on the results of this study.

Report

Consumers hypothesised that less than 30% of Brekky Blockz cereal packets contain a novelty token.

For a random sample of 40 Brekky Blockz cereal packets, 15% of the packets

contained a novelty token. This is lower than the 30% claimed by the food company,

and a Binomial test shows this difference is significant, n = 40, p = .024

The 95% confidence interval indicates that between 4% and 26% of Brekky Blockz

cereal packets contain a novelty token.

As expected, less than 30% of Brekky Blockz cereal packets contain a novelty token.

Example 2

In 2012, 22% of first -y ea r students studying Engineering at a particular university were

enrolled in their degree as part-time students. A student advisor believes the proportion of

first-year students currently studying Engineering at the university who are enrolled in their

degree part-time is now higher than this. She takes a random sample of 100 current first-

year Engineering students and records the enrolment status of each student (note that

enrolment status was coded 1 = part-time, 2 = full-time). She produces the following

output.

Write a report on the results of this study

A student advisor hypothesised that the percentage of current first-year students studying

Engineering at a particular university who are enrolled in their degree part time is higher

than it was in 2012, when 22% of first-year Engineering students at the university were

studying part-time.

For a random sample of 100 current first-year Engineering students at the university, 25% of

them were enrolled in their degree part-time. This is lower than the 22% of first-year

Engineering students at the university who were studying part-time in 2012, however a

Binomial test shows this difference is not significant, n = 100, p = .268

The 95% confidence interval indicates that between 17% and 33% of current first-year

Engineering students at the university are enrolled in their degree part-time.

There is no evidence to suggest the percentage of current first-year Engineering students at

the university who are studying part-time is higher than in 2012.

We have seen that a one-sample z-test or one-sample t-test can be used to test a hypothesis about a population mean, when we have access to a single sample of metric data.

If, however, we want to test a hypothesis about a population proportion, when we have access to a single sample of categorical data, it is appropriate to use a Binomial test.

As with the other types of hypothesis tests we have studied, in the formal hypothesis testing process we start by setting up null and alternative hypotheses and specifying the alpha level being tested at. We then obtain sample data and use either critical values or a p-value to make a decision about whether or not to reject the null hypothesis. However, the actual calculation of the test statistic is quite time-consuming when performing an exact Binomial test and is not covered in this unit. Instead, we look at the following alternatives:

1. SPSS will perform a Binomial test. In particular, it will perform a one-tailed Binomial test

unless the test proportion being compared against is 0.50, in which case it will perform a two-tailed test. We will see an example of running a one-tailed Binomial test in SPSS below and in this unit you will be required to solve problems of this type using SPSS.

1. When ≥ 10 and (1 − ) ≥ 10, we know from our previous work on sampling theory, that the sampling distribution of proportions is approximately normally distributed. Therefore, in such cases a one-sample z-test for proportions can be used. This has a very similar logic to the one- sample z-test for means that we have already covered previously, but the form of the hypotheses and the calculation of the actual z statistic are different. The hypotheses are set up in the same way as in the example we will show below for running a Binomial test in SPSS, but the z statistic for a wherêis the observed sample proportion, is the sample size and is the proportion value we are testing our data against. Normal distribution tables can then be used to determine the critical region and the observed z statistic calculated above is then reviewed, to see whether or not it is within the critical region. A decision is then made as to whether or not to reject H₀. In this unit we will not require you to carry out the above process. An advantage of this method though is that it is relatively straightforward to carry out either one-tailed or two-tailed tests of this type (which is determined, as usual, by the nature of the hypotheses being tested)

Exampleofrunning a one-tailed Binomial test using SPSS

To demonstrate this, we return to an example we first encountered in the lecture on sampling

distributions of proportions and see how to run a Binomial test for it. A newly established food company manufactures a cereal called Brekky Blockz. The company claims that 30% of packets of Brekky Blockz contain a bonus novelty token. However, some consumers suspect this claim is false - they believe that a lower percentage of the Brekky Blockz packets contain the novelty token. Use SPSS to run a Binomial test to investigate this, testing at a 5% significance level. First, note that in the actual formal hypotheses for the Binomial test, it is often convenient to rewrite a stated percentage as a proportion between 0 and 1. So here, 30% could be re-written as a proportion value between 0 and 1 by dividing by 100 (as 30% = 30/ 100 = 0.30) Step 1:Set up the null and alternative hypotheses and alpha level H₀: Population proportion ≥ 0.30 (The proportion of Brekky Blockz cereal packets that contain a token is not less than 0.30) H₁: Population proportion < 0 xss=removed>

The important part of this information is that we can see that the first coded category of the variable packet contains novelty token? is yes, and this category is coded 1. When we require you to run a Binomial test in SPSS in this unit, the file will always be set up in this way, with the first category being the one we are interested in. This is important as it allows us to specify the code for that first coded category as a ‘cut point’ for the Binomial test, as we will see on the next page.

To run the Binomial test itself, we then go to:

Analyze→ Nonparametric Tests → Legacy Dialogs →Binomial as shown below

We transfer the variable we are interesting in to the Test Variable List box (in this case, the variable Packet contains novelty token?)

We must then specify the test proportion. This is the value we are testing against with our null and alternative hypotheses (0.30 here as comparing our data against the proportion of 0.30 claimed by the cereal company)

We also must specify the cut point we are testing at, which is the number code given in the SPSS file to the first coded category which we are investigating. Here, the ‘yes’ category of interest was coded as 1 so we specify a cut point of 1.

Summary of Assessment Requirements 

Assessment Requirements

Introduction

• State the research problem.

• Formulate the alternative hypothesis clearly.

Sample Description

• Provide nature of the sample.

• Mention sample size and descriptive statistics (mean, SD, or proportions).

Comparison of Values

• Compare the sample mean with the reference mean (for t-tests).

• Compare the sample proportion with the claimed/reference proportion (for Binomial test).

Statistical Significance

• State whether the difference is significant or not.

• Quote test statistics (t, df, p for t-test; n and p for Binomial test).

95% Confidence Interval (CI) Interpretation

• Provide CI limits.

• Explain in plain words what the CI implies.

Conclusion

• Relate results back to the hypothesis.

• State whether the hypothesis is supported or rejected.

Academic Mentor’s Step-by-Step Guidance

Step 1 Understanding the Task

The mentor begins by helping the student carefully read the instructions. They explain the difference between a one-sample t-test (used for means) and a Binomial test (used for proportions). Together, they decide which test is appropriate based on the data type.

Step 2 Setting up the Hypothesis

The mentor explains how to construct null (H₀) and alternative (H₁) hypotheses. For example:

• H₀: The population mean = 8 hours of sleep

• H₁: The population mean ≠ 8 hours of sleep

Step 3 Describing the Sample

The mentor guides the student in reporting the descriptive statistics from SPSS:

• Sample size (n)

• Sample mean or proportion

• Standard deviation (if applicable)

Step 4 Running the Test in SPSS

The mentor walks the student through SPSS steps:

• For t-test: Analyze → Compare Means → One-Sample t-Test

• For Binomial test: Analyze → Nonparametric Tests → Legacy Dialogs → Binomial

Step 5 Interpreting SPSS Output

The mentor explains how to read key outputs:

• Test statistic (t, df, or n)

• Significance value (p)

• Confidence intervals

Step 6 Writing the Report

The mentor supports the student in drafting each section of the report, ensuring all required elements are included (introduction, results, CI interpretation, and conclusion).

Step 7 Linking Back to the Hypothesis

Finally, the mentor helps the student phrase the conclusion so it directly answers the research question — whether the alternative hypothesis is supported or not.

Final Outcome & Learning Objectives Covered

Assessment Outcome

By the end of the assessment, the student was able to produce a clear, statistically accurate, and well-structured report that addressed the hypothesis correctly.

Learning Objectives Achieved

• Understanding the purpose of hypothesis testing.

• Correctly setting up null and alternative hypotheses.

• Accurately interpreting SPSS outputs for both t-tests and Binomial tests.

• Applying correct statistical reporting format (APA style: reporting t, df, p, CI).

• Writing a structured report that communicates results effectively.

Unlock Your Academic Success with Expert Assignment Solutions

Looking for guidance on your assignment? You can download the sample solution below to see how a professional approach is structured. The sample is for reference only and should not be submitted as your own work, as doing so may result in plagiarism penalties.

Prefer a fully custom-written, plagiarism-free assignment? Our team of professional academic writers can craft a solution tailored to your requirements, helping you:

• Achieve original, high-quality content that meets academic standards

• Save time and focus on understanding key concepts

• Submit with confidence, knowing your work is 100% unique

Disclaimer: The sample provided is for reference and learning purposes. Plagiarism is strictly prohibited.

Take the next step in your academic journey:

[Download Sample Solution]                              [Order Fresh Assignment]