Problem 5 [15 points = 5 + 5 + 5] Academic advisors conduct a comparative study among two INDEPENDENTLY SELECTED groups of students about their intention to graduate within the next THREE years. Group I consisted of n1 = 200 students from Natural Science and Math (NSM) school and group II included n2 = 100 students who major in Business. It turned out that X1 = 111 NSM students and X2 = 69 Business majors plan to graduate. Answer YES means that response was positive. Below are the summaries. Group Size = n Yes = X Proportion NSM n1 = 200 X1 = 111 (p)1 = 111/200 = 0.555 Business n2 = 100 X2 = 69 (p)2 = 69/100 = 0.69 POOLED |n1 + n2 = 300 X1 + X2 = 180 p = 180/300 = 0.6 At the significance level a = 0.01, do you have enough evidence to conclude that the theoretical proportion in the NSM is LOWER than in Business? 1. Evaluate the Test Statistic 2. Specify the Critical Value 3. State the Rejection Rule After that, formulate your decision: whether you have enough evidence to reject the hypothesis about equality of theoretical proportions. IMPLEMENT the rejection rule. Solution