5.48 Work hours and education: The General Social Survey collects data on demographics, education, and work, among many other characteristics of US residents. Using ANOVA, we can consider educational attainment levels for all 1,172 respondents at once. Below are the distributions of hours worked by educational attainment and relevant summary statistics that will be helpful in carrying out this analysis.
Educational attainment
Less than HS (1)
HS (2)
Jr Coll (3)
Bachelor's (4)
Graduate (5)
Total
Mean
38.67
39.6
41.39
42.55
40.85
40.45
SD
15.81
14.97
18.1
13.62
15.51
15.17
n
121
546
97
253
155
1172
(a) Write hypotheses for evaluating whether the average number of hours worked varies across the five groups.
(b) Below is part of the output associated with this test. Fill in the empty cells (please be accurate to two decimal places).
Df
Sum Sq
Mean Sq
F value
Pr(>F)
degree
501.54
0.0682
residuals
267382
Total
(c) What is the value of the test statistic associated with this ANOVA test? (please round to two decimal places)
(d) What is the p-value associated with this ANOVA test? (please round to four decimal places)
(e) Interpret the conclusion of the test in the context of the study:
