57. Automobile Operation Cost. The Bureau of Transportation Statistics reports that the mean cost of operating an automobile in the United States, including gas and oil, maintenance and tires, is 5.9 cents per mile. Suppose that a sample taken this year of 100 automobiles shows a mean operating cost of 6.2 cents per mile, and assume that the population standard deviation is 1.5 cents per mile. Test whether the population mean cost is greater than 5.9 cents per mile, using level of significance .
9.2.57
(a) Since the sample size of is large (), Case 2 applies, so it is appropriate to apply the test. (b) Even though the sample mean cents per mile is greater than the hypothesized mean cents per mile, this is not enough by itself to reject the null hypothesis. It also depends on the variability of the data and on . (c) Since cents per mile is 2 standard errors above cents per mile, it is mildly extreme.