The 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-test that is appropriate.
b. Use the two-sample t-test, even though it is not appropriate.
c. Compare the results. The numerator of both t-values is the difference in sample means, which is 1.12 inches. What must be causing the different t-values if the numerators are the same?

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