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A random sample of size n = 100 from a normal population with unknown mean and variance is to be used to test the null hypothesis, H0 : μ = 12, versus the alternative, H0 : μ /= 12. The observed sample standard deviation is s = 0.5.

(i) Determine the rejection region for α = 0.1, 0.05 and α = 0.01.

(ii) If the true population mean has shifted to μ = 11.9, determine the value of β corresponding to each of the rejection regions obtained in (i) and hence the power of each test. Comment on the effect that lowering α has on the corresponding values of β and power.

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