Problem 4: 15 points = [8 + 7] - [ Educators compare students' satisfaction level using large samples from two groups. Group I included ni = 400 undergraduate students. Group II was formed by na 200 graduate ones. Summaries are presented in the table below. Group Size Satisfied Sample Proportion Undergraduate n = 400 Xi = 312 p. 312/400 = 0.78 Graduate n2 = 200 X2 = 138 ()2 = 138/200 = 0.69 1. At the significance level, a = 0.01, do you have evidence that population rates differ? 2. At the same significance level, do you have enough evidence to conclude that the satisfaction rate among undergraduate students is higher than for graduate ones? Show test statistic, critical value (values) and state rejection rules in each case. Solution