# (a) z = (108 – 100)/ v 36 = 1.33. The area in the tail beyond 1.33 is 9.18%, which isthe…

(a) z = (108 − 100)/√36 = 1.33. The area in the tail beyond 1.33 is 9.18%, which isthe probability of a Type I error.
(b) z = 1.64 cuts off 5% in the upper tail of the distribution, hence we need thedecision rule to be at X + 1.64 × s/√n = 100 + 1.64 × √ 36 = 109.84.
(c) Under H1: μ = 112, we can write X ~ N(112, 900/25). (We assume the same vari-ance under both H0 and H1 in this case.) Hence z = (108 − 112)/√36 = − 0.67.This gives an area in the tail of 25.14%, which is the Type II error probability.
Usually, however, we do not have a precise statement of the value of μ under H1so cannot do this kind of calculation.

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