Suppose we would like to compare a new treatment (treatment 1) to the standard treatment (treatment 2) in where treatment assignment will be done by permuted block randomization so that the two-sample t-test will be appropriate to compare these two treatments. Assume the population variance of the weight distribution is 64. We wish to detect a 5 unit weight difference between the new treatment and the standard treatment with 90% power at the significance level α = 0.05 using a two-sided t-test. (a) Find the necessary sample size for the study for the given design characteristics assuming equal allocation. (b) If the size of the treatment effect turned out to be what you expected, what is the p-value? (c) How large should the estimated treatment effect be to make the p-value significant (≤ 0.05)?

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