7. A committee studying employer-employee relations proposed that each employee would rate his or her immediate supervisor and in turn the supervisor would rate each employee. To find reactions regarding the proposal, 120 office personnel and 160 plant personnel were selected at random. Seventy-eight of the office personnel and 90 of the plant personnel were in favor of the proposal. To test the hypothesis that the population proportions are equal, what is the critical value using the 0.05 level of significance? 

8. A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal. At the 0.05 significance level, is there a difference in the mean yields of the two funds? What is the null hypothesis? 

9. High school students were interested in a teacher’s claim that the length of time (hours) that a student studies for a test, the higher the test score. The students collected the data and the teacher did the regression analysis with the following results (See the question file).   

To test the null hypothesis that the slope is zero, what are the t-test statistic and the t-critical value using the 0.05 significance level?