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 (treat this as completely randomized design):

Table 1: Weeks of Life

Brand1 Brand2 Brand3
100 96 92
96 92 76
75 84 82
108 100 96
98 100

Answer the questions based on the observed data

a. (5pt) Are the lives of these brands of batteries different?

b. (5pt) Analyze the normality assumption and state your conclusion.

c. (5pt) Check the constant variance assumption and state your conclusion.

d. (5pt) Construct 95% simultaneous confidence interval for all pairs of m eans using Tukey's method.

e. (5pt) From d, which brand has the shortest life?

f. (5pt) For the brand selected in (e), the manufacturer decides to replace without charge any battery that fails in less than 80 weeks, what percentage of batteries of this brand would the company expect to replace?