Question

A randomized clinical trial was designed to have power of 80% (i.e. Type II error probability of 20%) to detect a mean treatment effect of δ > 0 at the 5% level . We assume that the treatment effect values are normally distributed with the mean μ and the standard deviation σ = 10δ. Based on the research question, we can set both null and alternative hypotheses as follows: H0 :μ=0 vs. H1 :μ=δ. Find the sample size needed.

Answer 1

Let the sample size be n.

Standard error of mean, SE =

Given δ > 0, this is a right tail test.

Z value for 0.05 significance level is 1.645

Critical value to reject H0 is  

Power = P(Reject H0 | H1 is true) = 0.80

P( > | ) = 0.80

(Using Z tables)

(Rounding to next integer)