Suppose the prior used in Example 16.2 was changed to μ = N(22.35, .24) rather than N(22.52, .24) and the prior sample size used remains α = 10. How does this affect, if at all, WW's predicted rank? Compare the two results and, if a difference occurs, give an explanation for the difference.
Example 16.2
A competitive Division I NCAA college swimming team is practicing for the 2009 conference championship. In the womens' 50 yard freestyle, the college team has decided to have two heats. There are six swimmers in the first heat and six swimmers in the second heat. A swimmer (WW, say) competes in the first heat and her time is X1 seconds. The times X1, ... , X6 of the six swimmers in the first heat are given in Table 16.2. The team has decided that the six fastest swimmers in the two heats will be chosen to compete in the event at the conference championship. We wish to estimate WW's rank order among X1, ... , X12. Here r = 6 and n = 12.
