Lab 10 Hypothesis Tests, Confidence Intervals, and Chi-Square for Proportions
Instructions: Answer each of the following questions and include screenshots of your handwritten work to
support your answers. Your final submission should be a Word doc or a pdf. The questions should be done
with a group of 2-3 other students. List their names and a description of their contribution at the end of the
document.
Goals: The purpose of this lab is to explore two and more sample hypothesis tests, confidence intervals and
their properties. This lab focuses on how to perform one-sample hypothesis tests, confidence intervals, and
Chi-square tests for proportions.
1. Loading Data
Open “Fakedata.xlsx” as our data file for this lab.
2. One-sample hypothesis tests for proportions
Suppose that in our fake data we would like to test whether there are significant differences in the
proportions of males and females. In other words, we want to test the hypothesis:
H0: p = 0.50,
Ha: p ≠ 0.50.
We run this as a one sample test since these are not independent samples.
Include the output and a sentence stating the conclusion from this hypothesis test in your lab report.
Write out a one or two sentence summary of the results of this hypothesis test using the example
sentences in Lab 8.
3. One-sample confidence intervals for proportions
a. Confidence intervals can be computed as well:
b. Compute a 99% confidence interval predicting the actual proportion of females and include the
commands and the output in your lab report. Write out a one or two sentence summary of the
results of this confidence interval using the example sentences in Lab 7.
4. Chi-square test - Setup
Suppose we would like to know if there is a relationship between Gender and Favorite Color. That is, we
aim to test the hypotheses:
H0: There is no relationship between Gender and FavColor,
Ha: There is a relationship between Gender and FavColor.
a. Again, you should first construct the appropriate numerical and graphical summaries for each of
these groups. In lab 2 you constructed the appropriate summaries for a C-C relationship. Construct
those now and include them in your lab report.
b. Once you have constructed the appropriate summaries, you may notice that it appears that there
may be differences in the proportions in each row. We would like to implement a χ2-test to
determine if this is a significant difference.
5. Run the Chi-square test
a. Open the file “Chi-square 2x2 to 6x6.xlsx.” Click on the 4x4 tab at the bottom of the sheet. For this
lab, you should only type in the yellow cells.
Type in or paste the Gender by FavColor table values into the Observed section of the sheet. Be sure
to delete the entries which you will not be using in that section. Since there are four levels for
FavColor and two levels for Gender, the degrees of freedom is df = (4-1) × (2-1) = 3. Fill this in below.
Write a sentence about whether or not the expected cell counts meet the minimum requirements.
Scroll down to the end of the calculation to find the χ2 and p-values.
6. Summarizing the results of a Chi-square test
Finally, we will learn the appropriate way to summarize the results of a Chi-square test in a report. Should
you ever need to do this, you may want to look up APA format for statistical output, where you will find
many examples of how you should appropriately report statistical output. We will not get into all of the
details here on significant figures, but will practice the standard format. The output will be as follows,
where the blanks are filled in within the context of your test. Note that when using a test that has a
degrees of freedom, you should include those with your output.
A Chi-square test was run comparing ____verbal statement of Ho____ and
significant evidence that ____verbal statement of Ha_ ,
__ χ2(df) = insert value__, p-value = __value__.
there was or was not__
Application Questions
For this lab you will continue to use the Fakedata set. Answer each of the following questions. For questions
requiring a confidence interval write a one or two sentence answer stating the result in context. For
hypothesis tests, show all four steps of the test, substituting the appropriate values from your software
output. Include all commands and output in your lab report. No credit will be given without the software
output screenshots.
7. Construct a 95% confidence interval predicting the actual proportion who prefer grain for breakfast.
8. Determine whether there is significant evidence that the proportion who prefer fruit for breakfast is less
than 20%.
9. Is there a significant relationship between gender and the preferred breakfast?
10. Do not forget to compare your answers to the previous questions with your group. List the names of
your group and give a brief description of their contributions at the end of the document.