91Ó°ÊÓ

Sodium content. A researcher studied the sodium content in lager beer by selecting at random six brands from the large number of brands of U.S. and Canadian beers sold in a metropolitan area. The researcher then chose eight 12 -ounce cans or bottles of each selected brand at random from retail outlets in the area and measured the sodium content (in milligrams) of each can or bottle. The observations follow. $$\begin{array}{cccccccc} & & & & i\\\ \hline i & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline 1 & 24.4 & 22.6 & 23.8 & 22.0 & 24.5 & 22.3 & 25.0 & 24.5 \\ 2 & 10.2 & 12.1 & 10.3 & 10.2 & 9.9 & 11.2 & 12.0 & 9.5 \\ . . & . . & . . & . . & . . . & & & . . & . . \\ 6 & 21.3 & 20.2 & 20.7 & 20.8 & 20.1 & 18.8 & 21.1 & 20.3 \end{array}$$ Assume that ANOVA model (25.1) is applicable. a. Test whether or not the mean sodium content is the same in all brands sold in the metropolitan area: use \(\alpha=.01 .\) State the alternatives. decision rule, and conclusion. What is the \(P\) -value of the test? b. Estimate the mean sodium content for all brands; use a 99 percent confidence interval.