Detecting acid rain: power. Exercise 16.6 (page 394) concerned detecting acidrain

Chapter 0, Problem 16.16

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Detecting acid rain: power. Exercise 16.6 (page 394) concerned detecting acidrain (rainfall with pH less than 5) from measurements made on a sample of n daysfor several sample sizes n. That exercise shows how the P-value for an observedsample mean x changes with n. It would be wise to do power calculations beforedeciding on the sample size. Suppose that pH measurements follow a Normaldistribution with standard deviation = 0.5. You plan to test the hypothesesH0: = 5Ha: < 5at the 5% level of significance. You want to use a test that will almost alwaysreject H0 when the true mean pH is 4.7. Use the Power of a Test applet to find thepower against the alternative = 4.7 for samples of size n = 5, n = 15, andn = 40. What happens to the power as the size of the sample increases? Which ofthese sample sizes are adequate for use in this setting?