According to CNN business partner Careerbuilder.com, the average starting salary for accounting graduates in 2008 was at least $47,413. Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2008. Compute the power of the hypothesis test to reject the null hypothesis if the true average starting salary is only $47,000. Assume that the population standard deviation is known to be $4,600 and the test is to be conducted using an alpha level equal to 0.01.
A) 0.0872
B) 0.1323
C) 0.8554
D) 0.9812

Question

Quizplus · Accepted Answer

The power of the hypothesis test is the probability of rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the average starting salary for accounting graduates in 2008 is at least $47,413. The alternative hypothesis is that the average starting salary is less than $47,413.The power of the hypothesis test can be calculated using the following formula:Power = 1 - Betawhere Beta is the probability of failing to reject the null hypothesis when it is false.Beta can be calculated using the following formula:Beta = P(Z < z)where Z is the standard normal random variable and z is the critical value for the test.In this case, the critical value for the test is -2.326. The standard normal random variable can be calculated using the following formula:Z = (x - mu) / sigmawhere x is the sample mean, mu is the population mean, and sigma is the population standard deviation.In this case, the sample mean is $47,000, the population mean is $47,413, and the population standard deviation is $4,600.Substituting these values into the formula, we get:Z = (47,000 - 47,413) / 4,600 = -0.896Substituting this value into the formula for Beta, we get:Beta = P(Z < -0.896) = 0.1867Substituting this value into the formula for Power, we get:Power = 1 - Beta = 1 - 0.1867 = 0.8133Therefore, the power of the hypothesis test is 0.8133.

According to CNN Business Partner Careerbuilder