Question

In: Statistics and Probability

1. Below is a contingency table for the certain majors and the number of hours studied...

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).

Solutions

Expert Solution

orchestra answered 1 year ago
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