Exercise 12 uses Data Set 23 "Old Faithful" in Appendix B, and the sample size is 250.
a. If we have sample paired data with 250 nonzero differences, what are the smallest and largest possible values of T?
b. If we have sample paired data with 250 nonzero differences, what is the expected value of T if the population consists of matched pairs with differences having a median of 0?
c. If we have sample paired data with 250 nonzero differences and the sum of the positive ranks is 1234, find the absolute value of the sum of the negative ranks.
d. If we have sample paired data with n nonzero differences and one of the two rank sums is k, find an expression for the other rank sum.