4) The investigators plan to repeat this experiment on freshman undergraduates. Prior studies suggest that the s.d. = 15 units of productivity.A difference of 15 points is considered important.

a) If the investigators say that the most important contrast is the difference between the control and the average of the four other treatments (i.e., the contrast in part b), what sample size is needed to get 80% power for a difference of 15? Assume alpha = 5%.

b) If the investigators tell you that the most important contrast is the difference between treatments C and D, what sample size is needed to get 80% power for a difference of 15? Assume alpha=5%.

c) Assume the investigators do not specify any a-priori contrasts. Instead, they are interested in all pairwise differences. Since there are 10 possible differences, you need to adjust for multiple comparisons. Although Tukey is the standard multiple comparisons procedure for all pairwise differences, it's a little hard to implement. It is closely approximated by a Bonferroni correction, i.e. you test each of the 10 pairwise differences using alpha = 0.05 / 10 = 0.005. What sample size is needed to get 80% power for when the difference between a pair of treatments is 15? Assume the alpha for each test = 0.