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.
