Question: Sleeping pills Sleeping Hours A1 A2 A3 6.2 6.1 6.0 6.3 6.1 5.9 6.3 6.5 6.7 6.6 6.1 6.4 6.8 5.9 6.6 6.8 6.9

Sleeping pills Sleeping Hours A1 A2 A3 6.2 6.1 6.0 6.3 6.1

Sleeping pills Sleeping Hours A1 A2 A3 6.2 6.1 6.0 6.3 6.1 5.9 6.3 6.5 6.7 6.6 6.1 6.4 6.8 5.9 6.6 6.8 6.9 6.6 A4 6.4 6.4 6.2 6.3 7.0 5.9 There was an animal clinical trial aiming to study the difference among four kinds of sleeping pills: A1, A2, A3, A4. 24 healthy rabbits were chosen and were randomly assigned to take one of the four pills. The number of sleeping hours are recorded in the above table for each rabbit. 1. Calculate the between group sum of squares: (Please round to 2 significant figures.) 2. Calculate the within group sum of squares: (Please round to 3 significant figures.) 3. Consider the following hypothesis with a = 0.05 Ho : HA1 = HA, = HAs = HA4 vs H1 : HA, + HA, for some i + j What is the p-value? (Please round to 3 significant figures.) 4. Conduct a multiple comparison with Bonferroni adjustment: o What is p-value for comparing the population means between Aj and A2: . (Please round to 2 significant figures.) Should we reject the null hypothesis? (Yes or No) o What is p-value for comparing the population means between A3 and A1: . (Please round to 2significant figures.) Should we reject the null hypothesis? (Yes or No)

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