Chapter 9, Problem 94CRE

Parents The following table shows the heights (in inches) of a random sample of students and their parent of the same gender. Test the hypothesis that the mean for the students is more than the mean for the parents, at the $0.05$ level. Assume the data are Normal.

a. Use the paired $t\text{-test}$ that is appropriate.

b. Use the two-sample $t\text{-test}$, even though it is not appropriate.

c. Compare the results. The numerator of both $t\text{-values}$ is the difference in sample means, which is $1.12$ inches. What must be causing the different $t\text{-values}$ if the numerators are the same?