An experiment was carried out in a completely randomized design to compare the differences in the levels of physiologically active polyunsaturated fatty acids (PAPUFA, in percentages) of six different brands of diet margarine, resulting in the following data (Devore 1982):

Imperial 14.1 13.6 14.4 14.3 Parkay 12.8 12.5 13.4 13.0 12.3 Blue Bonnet 13.5 13.4 14.1 14.3 Chiffon 13.2 12.7 12.6 13.9 Mazola 16.8 17.2 16.4 17.3 18.0 Fleischmann’s 18.1 17.2 18.7 18.4 Prepare and run a SAS program to obtain the output necessary to provide all of the following information. You must extract numbers from the output and write answers on a separate sheet of paper.

a. Assuming the fixed effects one-way classification model for these data, give estimates of true mean PAPUFA percentages μ1, μ2, μ3,

μ4, μ5, and μ6 and the error variance σ2. Write down the corresponding analysis of variance table including the p-value. State the hypothesis tested by the F-statistic and your decision based on the p-value.

b. Mazola and Fleischmann’s are corn based, and the others are soybean based. Use an appropriate contrast statement to compute an F-statistic for testing the hypothesis that the average of true mean PAPUFA percentages for corn-based brands is the same as the average for soybean-based brands. Include the corresponding sum of squares and the F-statistic in the above ANOVA table. Based on the p-value, state your conclusions from the experiment in words.

c. Compute Tukey 95% confidence intervals for all pairwise differences in true mean PAPUFA percentages, i.e., (μr − μs)s. Explain why these intervals are wider than the t-distribution based 95% confidence intervals (other than the fact that the Tukey percentiles are larger than the corresponding t values).