Let 11, 12 be i.i.d. N(μ, σ^2) and Yn be i.i.d. N(ν, σ^2). We wish to test the two-sided null hypothesis:
Ho: μ = ν
Find the sample size that provides 90% power for testing the null hypothesis assuming an alternative hypothesis of Ha: μ ≠ν, σ = 10, and a two-sided type-I error rate of 0.05. Consider a group sequential design using two-sided O'Brien-Fleming boundaries with k = 3. Provide the critical values, maximum sample size, expected sample size under the null, and expected sample size under the alternative.
(c) Consider a group sequential design using two-sided Pocock boundaries with k = 3. Provide the critical values, maximum sample size, expected sample size under the null, and expected sample size under the alternative.
(d) Consider a group sequential design using two-sided Wang and Tsiatis boundaries with σ = 0.25 and k = 3. Provide the critical values, maximum sample size.