The skid properties of a snow tire have been tested, and a mean skid distance of 47 m has been established for standardized conditions. A new, more expensive tire is developed, but tests on a sample of 17 new tires yield a mean skid distance of 45 m with a standard deviation of 3.7 m. Because of the cost involved, the new tires will be purchased only if it can be shown at the α = 0.005 significance level that they skid less than the current tires. Based on the sample, will the new tires be purchased?
Use the traditional approach summarized. Draw a graph showing the test statistic and critical values. In each case, assume that the population has a distribution that is approximately normal and that the sample is randomly selected.