is unbiased) can be rejected at the 1% level. Р3.9. Denote the life of a light bulb from the new process by Y. The mean of Y is and the standard Р deviation of Y is Y 200 hours. Y is the sample mean with a sample size n 100. The Р 200Р standard deviation of the sampling distribution of Y is Y 20 hours. The Р Y n 100Р hypothesis test is H0:2000 vs. H1 2000 . The manager will accept the alternative Р hypothesis if Y 2100 hours. Р (a) The size of a test is the probability of erroneously rejecting a null hypothesis when it is valid. Р The size of the manager’s test is Р size Pr(YY 2100| 2000) 1 Pr( 2100| 2000)Р Y 2000 2100 2000Р 1 Pr| 2000 Р 20 20Р 1 (5) 1 0 999999713 2 87 107 ,Р ©2011 Pearson Education, Inc. Publishing as Addison Wesley