John Daum and Chris Yin are star swimmers at a local college. They are preparing to compete at the NCAA Division II national championship meet, where they both have a good shot at earning a medal in the men's 100-meter freestyle event. The coach feels that Chris is not as consistent as John, even though they clock about the same average time. In order to determine if the coach's concern is valid, you clock their time in the last 20 runs and compute a standard deviation of 0.85 seconds for John and 1.20 seconds for Chris. It is fair to assume that clock time is normally distributed for both John and Chris.
a. Specify the hypotheses to test if the variance of time for John is smaller than that of Chris.
b. Carry out the test at the 10% level of significance.
c. Who has a better likelihood of breaking the record at the meet? Explain.