STAT 110: Homework 5 Solutions
Spring 2016
Methicillin-resistant staphylococcus aureus (MRSA) is a common bacterium that is primarily spread through skin to
skin contact. It can also be spread through skin-contaminated object contact (e.g., if an infected person’s skin comes
into contact with equipment at the gym, MRSA could spread to another person’s skin if it also comes into contact with
this equipment). To determine whether gym users were more likely to test positive for MRSA, researchers collected
data on 960 college students. They were surveyed about their gym use and tested for MRSA. The results are
summarized in the table below.
Used the gym
Did not use the gym
Total
Test positive for MRSA
203
25
228
Test negative for MRSA
512
220
732
Total
715
245
960
1. Find the proportion of students who used the gym that tested positive for MRSA. (2 pts)
203 / 715 = .284
2. Find the proportion of students who did not use the gym that tested positive for MRSA. (2 pts)
25 / 245 = .102
3. Sketch in the mosaic plot on the graph below. (1 pt)
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4. Next, you will investigate this question: Do the data provide statistical evidence that the proportion
testing positive for MRSA is greater for those students who used the gym than for those who didn’t?
Your solution should include the p-value for investigating this question and a conclusion written in
everyday language. (4 pts)
p-value: <.0001
Conclusion: The study provides statistical evidence that the proportion testing positive for MRSA is
greater for those students who used the gym than for those who didn’t use the gym.
Next, the results were tabulated according to whether or not the student had ever lived in a dorm and are
summarized in the following contingency table.
Has lived in dorm
Never lived in dorm
Total
Test positive for MRSA
200
28
228
Test negative for MRSA
556
176
732
Total
756
204
960
5. Find the proportion of students who have lived in a dorm that tested positive for MRSA. (2 pts)
200 / 756 =.265
6. Find the proportion of students who have never lived in a dorm that tested positive for MRSA. (2 pts)
28 / 204 = .137
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7. Sketch in the mosaic plot on the graph below. (1 pt)
8. Next, you will investigate this question. Do the data provide statistical evidence that the proportion
testing positive for MRSA differs between those students who have and have not lived in a dorm?
Your solution should include the p-value for these data and a conclusion written in everyday language.
(4 pts)
p-value: .0001 (from Fisher’s exact test) or <.0001 (from chi-square test)
Conclusion: The data provide statistical evidence that the proportion testing positive for MRSA
differs between those students who have and have not lived in a dorm.
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Finally, the results were tabulated according to sex. The mosaic plot for these data is shown below.
9. Suppose you are interested in testing whether the proportion that test positive for MRSA differs
between men and women. On the following mosaic plot, sketch in hypothetical results that would
produce a smaller p-value than what would be obtained from the results shown in the mosaic plot
above. (1 pt)
One possible answer is shown below. The big idea is that if the p-value is smaller, you should see a
bigger difference between the proportions testing positive across each gender.
10. On the following mosaic plot, sketch in hypothetical results that would indicate that there was no
difference in the proportion testing positive for MRSA across sex. (1 pt)
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