Problem 2: Three brands of batteries are under study. It is suspected that the lives in weeks) of the three brands are different. Five randomly selected batteries of each brand are tested with the following results: Weeks of Life Brand 1 Brand 2 Brand 3 100 76 108 96 80 100 92 75 96 96 84 98 92 82 100 1. Are the mean lives of these brands of batteries different? Use a = 0.02 (15 points) 2. Construct a 95 percent confidence interval estimate on the mean life of battery brand 2. Construct a 99 percent confidence interval estimate on the mean difference between the lives of battery brands 2 and 3 (15 points)