Question

Could the number of hours a person spends studying be related to whether or not they have a roommate? At a local summer camp, a simple random sample of 100 attendees was selected. Data was collected on each attendee on how many hours they spend studying per week and whether they have a roommate. The data was then presented 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: What proportion of attendees have a roommate and study for at least 5 hours per week? Also, what proportion of attendees do not have a roommate and study for at least 5 hours per week? (2 points)

Part B: Explain the association between the number of hours spent studying per week and whether they have a roommate for the 100 camp attendees. Use the data presented in the table and proportion calculations to justify your answer. (4 points)

Part C: Perform a chi-square test for the hypotheses.

H₀: The number of hours spent studying per week by attendees at a local summer camp and whether they have a roommate have no association.
H_a: The number of hours spent studying per week by attendees at a local summer camp and whether they have a roommate have an association.

What can you conclude based on the p-value? (4 points)

Answer 1

(a) The proportion of students who have a roommate and stude at least 5 hours (5 hours or more) per week = (26 + 14) /100 = 40/100 = 2/5

(b) It seems that students who have a roommate tend to put in more hours of study per week

(c) The Eexpected value tables are as below.

Each Expected Value = (Row Total * Column Total) / N, Where N = Total Observations

Expected
	None One	Female	Total
Three	13.50	16.50	30
Five	20.70	25.30	46
> 5	10.80	13.20	24
Total	45.00	55.00	630

The Test Statistic:

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
A	15	13.50	1.50	2.25	0.166667
B	20	20.70	-0.70	0.49	0.023671
C	10	10.80	-0.80	0.64	0.059259
D	15	16.50	-1.50	2.25	0.136364
E	26	25.30	0.70	0.49	0.019368
F	14	13.20	0.80	0.64	0.048485
Total					0.453813

as found above = 0.45

The degrees of freedom, df = (r – 1) * (c -1) = (2 - 1) * (3 - 1) = 1 * 2 = 2

The p value: The p value at = 0.45, df = 2, is P value = 0.7985.

The Decision Rule: If p value is < , Then Reject H0.

The Decision: Since p value (0.7985) is > (0.05), We Fail To Reject H0.

The Conclusion: There is insufficient evidence at the 95% significance level to conclude that the number of hours spent studying per week and whether they have a roommate has an association.