A professor at a large university is interested in determining whether students who have a roommate is associated with the number of hours they are able to study for classes. A simple random sample of 100 students in the university was taken, and each student was asked the following two questions:

1. Do you currently have a roommate?
2. How many hours do you study per week?

The responses of the 100 students are summarized in the frequency table.

Hours Studied Per Week
Roommate Status
Total
No Roommate
One Roommate
Three
15
15
30
Five
20
26
46
More than five
10
14
24
Total
45
55
100
Part A: Calculate the proportion of students in the sample who have a roommate and who study for at least five hours. Also, calculate the proportion of students in the sample who do not have a roommate and who study for at least five hours. (5 points)

Part B: The responses of the 100 students are summarized in the segmented bar graph shown.

A horizontal bar chart is shown with two bars, One Roommate and No Roommate; separated into three sections, Three Hours, Five Hours, More Than Five Hours. Section percentages are for One Roommate, three hours, 27 percent; for One Roommate, five hours, 47 percent; for One Roommate, more than five hours, 26 percent; and for No Roommate, three hours, 33 percent; No Roommate, five hours, 45 percent and for No Roommate, more than five hours, 22 percent.

Write a few sentences summarizing what the graph reveals about the association between roommate status and the amount of hours studied each week among the 100 students in the sample. (5 points) (10 points)