Consider two independent samples {x1, x2, · · · , xn} from population N(µ1, ?2 1 ) and {y1, y2, · · · , yn} from population N(µ2, ?2 2 ) respectively. We wish to test the following hypotheses:

H0 : µ1 = µ2 vs H1 : µ1 > µ2.

Assume ?1 = ?2 = ? = 1. Find the powers of the z-test (from introductory statistics course) in the following cases:

(i) the powers to detect a difference of µ1 ? µ2 = 0.1 and sample sizes are n = 9, 25, 100 respectively;

(ii) the powers to detect a difference of µ1 ? µ2 = 0.5 and sample sizes are n = 9, 25, 100 respectively;

(iii) the powers to detect a difference of µ1 ? µ2 = 1.0 and sample sizes are n = 9, 25, 100 respectively;

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