SECTION 6.131593.increase. If the level increases, the probability of rejectingH0increases, so in particular, the probability ofrejectingH0when it is false increases.5. (a)H0:μ50 000 versusH1:μ50 000.H1is true, since the true value ofμis 49,500.(b) The level is the probability of rejectingH0when it is true.UnderH0,Xisapproximatelynormallydistributedwithmean50,000andstandarddeviationσX5000100500.The probability of rejectingH0isPX49 400 .UnderH0, thez-score of 49,400 isz49 40050 0005001 20.The level of the test is the area under the normal curve to the left ofz1 20.Therefore the level is 0.1151.The power is the probability of rejectingH0whenμ49 500.Xis approximately normally distributed with mean 49,500 and standard deviationσX5000100500.The probability of rejectingH0isPX49 400 .Thez-score of 49,400 isz49 40049 5005000 20.The power of the test is thus the area under the normal curve to the left ofz0 20.Therefore the power is 0.4207.(c) Since the alternate hypothesis is of the formμμ0, the 5% rejection region will be the region
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