1) What is the critical value of t for the claim that the difference of two means is less than zero with α = 0.025 and sample sizes of nine and seven? Assume equal population standard deviations.
2) A committee that is 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 test if the reactions to the survey for office and plant personnel were the same, 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 propotions are equal, what is the critical value using the 0.05 level of significance?