1. Three brands of batteries are under study. It is suspected that the mean lives 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 (a) Is there evidence to suggest that the mean lives of these brands of batteries are different? Test an appropriate hypothesis at level a = 0.05. (b) Analyze the residuals from the data and state your conclusions. (c) Construct a 95 percent confidence interval for the mean life of battery brand 2. (d) Construct a 99 percent confidence interval for the difference be- tween the mean lives of brands 2 and 3. (e) Based on the data, which of the 3 brands has the longest mean life? (f) If the manufacturer will replace without charge any battery that fails in less than 85 weeks, what percentage of batteries would the company expect to replace for the brand you chose in (e)