## Description

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

α = 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 between 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)?

2. Consider testing the equality of the means of two normal populations,

where the variances are unknown but are assumed to be equal. The

appropriate test procedure is the pooled t-test. Show that the square

of the t-statistic is equal to the ANOVA F-statistic.