A researcher studies the sodium content in lager beer by selecting at random six brands from the large number of brands of U.S. and Cana- dian 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 are included in the file beer.txt, with sodium content in the first column and brand in the second col- umn. Please carry data analysis to test whether or not the mean sodium content is the same in all brands sold in the metropolitan area. Use SAS and provide SAS codes.

a. Should a random or fixed effects model be considered? State your

reason.

b. Test whether or not the mean sodium content is the same in all brands sold in the metropolitan area ( = 0.01). State both null and alternative hypotheses, decision rule, and conclusion. What is the p-value of the test?

c. What's the intraclass correlation coefficient? Interpret its value.

d. Estimate the mean sodium contents for all brands, and its 99%

confidence interval.

Datset:

Brand 1 2 3 4 5 6 7 8

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

3 19.2 19.4 19.8 19.0 19.6 18.3 20.0 19.4

4 17.4 18.1 16.7 18.3 17.6 17.5 18.0 6.4

5 13.4 15.0 14.1 13.1 14.9 15.0 13.4 14.8

6 21.3 20.2 20.7 20.8 20.1 18.8 21.1 20.3