According to CNN business partner Careerbuildercom the avera

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

Possible Answers:

0.8554

0.0872

0.9812

0.1446

Please Show your work.

Solution

Set Up Hypothesis
Null H0: U>=47413
Alternate Hypothesis H1: U<47413 ( left tailed - test)
Test Statistic
Population Mean(U)=47413
Standard Deviation(S.D)=4600
Number (n)=200
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=x-47413/(4600/Sqrt(200)
Zo = x-47413/325.269
Critical Value
The Value of Z at LOS 0.01% is -2.33

=> x-47413/325.269 = -2.33
=> x = 46655.123

The true population is given as 47000
P( Z <=x-U/(s.d/Sqrt(n)) = P( Z <= 46655.123-47000/(4600/Sqrt(200)
                       = P( Z <= -1.0602)
                       = 0.1446 [ANSWER]