Question

1. Below is a contingency table for the certain majors and the number of hours studied for
each major. The expected values are given in parentheses.
Rows: Hours/week

	humanities	social science	business	engineering	total
0-10	68 (88.67)	106 (90.05)	131 (106.6)	40 (59.69)	345
11-20	119 (110.5)	103 (112.2)	127 (132.9)	81 (74.39)	430
>20	70 (57.83)	52 (58.73)	51 (69.53)	52 (38.93)	225
total	257	261	309	173	1000

Chi-Square test for independence:

measure	DF	value	p-value
Chi-Square	6	34.63775	<0.0001

a) State the null and alternative hypotheses.

b) Report the test statistic and using a significance level of 0.05, give a conclusion based on
the p-value.

c) In the table below calculate the observed value minus the expected value (O-E) for each
cell.

	humanities	social science	business	engineering
0-10	68-88.67= -20.7
11-20
>20

d) Based on the table in c), which majors had more people than expected say they study
more than 20 hours/week? Which majors had more than expected saying that they study
0-10 hours/week?

2. The Health, Aging, and Body Composition study is a 10-year study of older adults. A research project
based on this study examined the relationship between education and pet ownership. The data
collected included information concerning pet owner characteristics and type of pet owned. The
following table gives the breakdown of pet ownership by education. In parentheses are the expected
values. The results of the chi-square test of independence are also given.

	non pet owners	dog owners	cat owners	total
less than HS	421 (431.46)	93 (73.25)	28 (37.29)	542
HS graduate	666 (641.61)	100 (108.93)	40 (55.46)	806
postsecondary	845 (858.93)	135 (145.82)	99 (74.25)	1079
total	1932	328	167	2427

Chi-Square test:

statistic	DF	value	p-value
Chi-Square	4	23.146832	0.0001

a) State the null and alternative hypotheses.

b) Using a significance level of 0.05, give a conclusion in context of the problem.

c) Compute the residuals in the table below.

	non pet owners	dog owners	cat owners
less than HS
HS graduate
postsecondary

d) Write a few sentences summarizing the table in c).

Answer 1