SLIX wax is developing a new high performance fluorocarbon wax for cross country ski racing designed to be used under a wide variety of conditions. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time to finish their standard test course should be less than 55 seconds for the former Olympic champion who is now their consultant. To test it, the consultant will ski the course 8 times.
a) The champion’s times are 56.3, 65.9, 50.5, 52.4, 46.5, 57.8, 52.2, and 43.2 seconds to complete the test course. Should they market the wax? Explain.
b) Suppose they decide not to market the wax after the test, but it turns out that the wax really does lower the champion’s average time to less than 55 seconds. What kind of error have they made? Explain the impact to the company of such an error.