Question

10. A recent study of higher education measured the pro- portion of college students who work in off-campus jobs for at least 20 hours a week. Four samples, each composed of 200 randomly selected students, were used to represent four types of institutions: large four-year state schools, small four-year state schools, large four-year private schools, and small four-year private schools. In the sample of 200 students from large state schools, 30 had such an off-campus job (15%), as compared to 24 (12%) in the sample of stu- dents from small state schools. In the large private school sample, the number was 42 (21%), as com- pared to 32 (16%) in the sample of students from small private schools. Use the chi-square distribution to test the hypoth- esis that the proportion of students who work in off-campus jobs for at least 20 hours a week is the same across all four institutional categories. Use a significance level of 1%.

Answer 1

Mo: Proportion of students who work in off campus jobs for atleast 20 hours a week is same across all 4 institutional categories H, Propostion i not same across all u institutional categories Under to (0) Observed frequency | Expected frequency (E) 2 30 N/y = 32 2.) 24 N/4 = 32 3) 42 N/4 = 32 4.) 32 N/4 = 32 N = 128 N= 128 test statistic - ( Oi- Eile ng 4-1 =3 = 5.25 p-value = P ( x 3 > 5.25) = 0.15 4 p-value > 2=0.01 - we fail to reject to There is not sufficient evidence to reject the claim that proportion of students who work in off compus jobs for at least 20 hours a week is same across all 4 institutional Categories