The following data are taken from three different populations known to be normally distributed, with equal population variances based on independent simple random samples.

(a) Test the hypothesis that each sample comes from a population with the same mean at the a = 0.05 level of significance. That is, test H0: µ1 = µ2 = µ3.
(b) If you rejected the null hypothesis in part (a), use Tukey's test to determine which pairwise means differ using a family wise error rate of a = 0.05.
(c) Draw boxplots of each set of sample data to support your results from parts (a) and (b).

Sample 1 Sample 3 Sample 2 35.4 42.0 43.3 39.4 48.6 35.0 39.2 33.4 42.0 53.9 44.8 35.1 36.9 32.4 46.8 28.9 22.0 51.7