Refer to the example concerning average sound intensity on page 260 . Calculate the power at \(\mu_{1}=77\) when

(a) the level is changed to \(\alpha=0.03\).

(b) \(\alpha=0.05\) but the alternative is changed to the twosided \(H_{1}: \mu eq 75.2\).

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EXAMPLE 22 Determining the probability of a Type II error-one-sided test We want to investigate a claim about the average sound intensity of certain vac- uum cleaners. Suppose the sound is a random variable having a normal distribution with a standard deviation of 3.6 dB. Specifically, we shall want to test the null hy- pothesis = 75.20 against the alternative hypothesis > 75.20 on the basis of measurements of the sound intensity of n = 15 of these machines. If the probability of a Type I error is to be = 0.05, what is the probability of a Type II error for 77.00 dB?