According to the Environmental Protection Agency (EPA) Fuel Economy Guide, the 2009 Honda Civic automobile obtains a mean of 36 miles per gallon (mpg) on the highway. Suppose Honda claims that the EPA has underestimated the Civic's mileage. To support its assertion, the company selects n = 50 model 2009 Civic cars and records the mileage obtained for each car over a driving course similar to the one used by the EPA. The following data result: x = 38.3 mpg, s = 6.4 mpg.

a. If Honda wishes to show that the mean mpg for 2009 Civic autos is greater than 36 mpg, what should the alternative hypothesis be? The null hypothesis?

b. Do the data provide sufficient evidence to support the auto manufacturer's claim? Test, using α = .05. List any assumptions you make in conducting the test.

c. Calculate the power of the test for the mean values of 36.5, 37.0, 37.5, 38.0, and 38.5, assuming that s = 6.4 is a good estimate of s.

d. Plot the power of the test on the vertical axis against the mean on the horizontal axis. Draw a curve through the points.

e. Use the power curve of part d to estimate the power for the mean valueµ= 37.75. Calculate the power for this value of m, and compare it with your approximation.

f. Use the power curve to approximate the power of the test whenµ= 41. If the true value of the mean mpg for this model is really 41, what (approximately) are the chances that the test will fail to reject the null hypothesis that the mean is 36?