We presented data for an experimental drug that was meant to increase HDL cholesterol. The data are represented in Table 13 for convenience.

(a) HDL cholesterol levels are known to have a distribution that is approximately normal. Verify that the largest sample standard deviation of any cell is no more than twice the smallest sample standard deviation of any cell.

(b) Use Minitab to test whether there is an interaction effect between the drug dosage and age.

(c) If the null hypothesis of no interaction is not rejected, determine whether there is sufficient evidence to conclude that the mean increase in HDL cholesterol is different (i) among each drug dosage group, (ii) for each age group.

Approach We use Minitab to obtain the two-way ANOVA. The steps for performing two-way ANOVA using Minitab and StatCrunch are given in the Technology Step-byStep on page 690. If the \(P\)-value corresponding to each hypothesis is small (say, less than \(\alpha=0.05\) ), reject the null hypothesis in favor of the alternative hypothesis.

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Table 13 Age Placebo Drug Dosage 5 mg 10 mg 18 to 39 years 4 3 -1 9 5 6 14 12 10 40 or older 3 2 0 3 6 7 10 8 7