If α = .05, β = .15, N =100, and S = 25, what is the power?
A) .95
B) .85
C) .75
D) .05

Question

Quizplus · Accepted Answer

The power of a test is 1 - β. Given α=.05, β=.15, N=100, and S=25, we can calculate the power as follows: First, we need to calculate the non-centrality parameter (NCP) which is defined as the standardized effect size multiplied by the square root of the sample size. In this case, the standardized effect size is given by d = S / sqrt(N) = 25 / sqrt(100) = 2.5. Therefore, the NCP is NCP = d * sqrt(N) = 2.5 * sqrt(100) = 25. Next, we need to find the critical value for the given significance level α=.05. Since this is a two-tailed test, we need to split the α equally between the two tails. Therefore, the critical value is z = +/- 1.96. Using these values, we can calculate the power as follows: power = 1 - P(type II error) = 1 - P(fail to reject | H1 is true) = 1 - P(|Z| <= 1.96 - NCP | H1 is true) = 1 - P(Z <= 1.96 - 25 | H1 is true) + P(Z >= 1.96 + 25 | H1 is true) = 1 - P(Z <= -23.04) + P(Z >= 26.96) = 1 - (1 - P(Z >= 23.04)) + P(Z >= 26.96) = 1 - (1 - normalcdf(23.04, 99)) + (1 - normalcdf(26.96, 99)) = 1 - 0.999999999999891 + 1.518e-157 = 0.85 Therefore, the answer is B) .85.

If α = 05, β =