Question: According to the Environmental protection Agency Fuel Economy Guide, the 2003 Honda Civic automobile obtained a mean of 38 miles per gallon on the highway. Suppose Honda Claims that the EPA has underestimated the Civic’s mileage. To support its assertion, the company select 36 model 2003 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 resulted: x= 40.3 mpg, s= 6.4 mpg.

a) if Honda wishes to show that the mean mpg for 203 Civic auto is greater than 38 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 a = .05. List any assumptions you make in conducting the test.

c) Calculate the power of t he test for the mean values of 38.5, 39., 39.5, 40.0. and 40.5, assuming 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) Using the power curve of part d to estimate the power for the mean values µ = 39.75. Calculate the power for this value of µ , and compare it to approximation.

f) Use the power curve to approximate the power of the test when µ =43. if the true value of t he mean mpg for this model is really 43, what ( approximately) are the chances that the test will fail to reject the null hypothesis that the mean is 38.