Suppose that we wish to test H 0 : = 0 versus H 1 :

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Suppose that we wish to test H0: μ = μ0 versus H1: μ ≠ μ0 where the population is normal with known σ. Let 0 < e < α, and define the critical region so that we will reject H0 if z0 > zε or if z0, − zα−ε, where z0 is the value of the usual test statistic for these hypotheses.

(a) Show that the probability of type I error for this test is α.

(b) Suppose that the true mean is μ1 = μ0 + δ. Derive an expression for β for the above test.

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Applied Statistics And Probability For Engineers

ISBN: 9781118539712

6th Edition

Authors: Douglas C. Montgomery, George C. Runger

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