Problem 6 [15 points = 5 + 5 + 5] Students from two groups (STAT and HISTORY) were selected independently for a comparative study of their final exam performance. Individual records were assumed normally distributed with unknown pa- rameters. Academic advisors suggested that two populations share ENTIRELY UNKNOWN EQUAL VARIANCES: [(1)2, (02)2]. Both samples were summarized and sample summaries are shown in the table below. Group Size = n Mean = X Variance = $2 V = $2 HISTORY n1 = 9 (X)1 = 65.8 ($1) 2 = 25.2 V1 = 25.2/9 = 2.8 STAT n2 = 9 (X)2 = 74.7 ($2)2 = 199.8 V2 = 199.8/9 = 22.2 At the significance level a = 0.05, do you have sufficient evidence that the population average performance among History classes is BELOW that in STAT? 1. Specify the Critical Value 2. Evaluate the Test Statistic Show the standard error and specify how many degrees of freedom you are going to use. 3. State and IMPLEMENT the Rejection Rule Solution 7