Consider again the one-way ANOVA hypothesis test described in Problem 9. Address the multiple comparison problem by applying the Bonferroni, Tukey, and Scheffé methods to obtain an overall confidence level of approximately 90%. Compare the widths of the confidence intervals generated with each of these methods with those of uncorrected 90% confidence intervals. Explain your findings. Recall that the relevant data are given in the file P12_9.XLS.

Data from in Problem 9

Assume that we gather independent random samples from large batches of each of three different brands of lightbulbs. We then record the lifetime of each selected bulb in the file P12_9.XLS. 

a. Test whether the different brands of lightbulbs have equal average lifetimes at the 10% significance level. 

b. Compute 90% confidence intervals for all pairs of differences between means. Which of these differences, if any, are significantly nonzero at the 10% significance level?