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A Test of the Mean of a Normal Distribution Against Two-Sided Alternative (Variance Known) The appropriate procedure for testing, at significance level o, the null hypothesis k19 H: A = 0 against the alternative hypothesis Hip to is obtained from the decision rule T-Mo reject Hy it IMO > Za/2 MO+ 2,2 / Vi In addition, the p-values can be computed by noting that the corresponding tail probability would be doubled to reflect a p-value that refers to the sum of the upper- and lower-tail probabilities for the positive and negative values of Z. The p-value for the two-tailed test is p-value = 200 > zwall Ho: pe = HD (9.5) where 2p/2 is the standard normal value associated with the smallest probability of rejecting the null hypothesis at either tail of the probability distribution pothesis Testing: Single Population Example 9.3 Analysis of Drill Hole Diameters (Hypothesis Test) The production manager of Circuits Unlimited has asked for your assistance in ana lyzing a production process. This process involves drilling holes whose diameters are normally distributed with a population mean of 2 inches and a population standard deviation of 0.06 inch. A random sample of nine measurements had a sample mean of 1.95 inches. Use a significance level of a = 0.05 to determine if the observed sample mean is unusual and therefore, that the drilling machine should be adjusted