Heights of Parents Data Set 2 in Appendix B includes the heights of parents of 20 males. If the difference in height for each set of parents is found by subtracting the mother’s height from the father’s height, the result is a list of 20 values with a mean of 4.4 in. and a standard deviation of 4.2 in. A histogram and a normal quantile plot suggest that the population has a distribution that is not far from normal.

a. Construct a 99% confidence interval estimate of the mean difference between the heights of the mothers and fathers.

b. Does the confidence interval include 0 in.? If a sociologist claims that women tend to marry men who are taller than themselves, does the confidence interval support that claim? Why or why not?