Use this paragraph to complete questions 1 and 2 below A car

Use this paragraph to complete questions 1 and 2 below. A car manufacturer claims that its vehicles average at least 30 miles per gallon, with a population variance of 4. We take a sample of 8 cars to test fuel efficiency, and wish to perform a hypothesis test on the car manufacturers claim at a level of =.975.

1.)The critical value for the sample mean X , below which we will reject the null hypothesis of 30 miles per gallon, is:

2.)Suppose the answer above is 29 (it isn’t, but assume it is for the following). Also, suppose the true population mean for fuel efficiency is 27.5 miles per gallon. Then, the Power of this hypothesis test is:

Solution

1) for alpha = 0.975

alpha / 2 = 0.4875

Z = 0.03 = x - 30   / [4 / srqt (8)]

x=30.04

critical value will be : 30.04

2)

Z = 29 - 27.5 / [4 /srqt(8) ]

Z = 1.06

probability = 0.1446

power = 1 - 0.1446 = 0.8554