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-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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Height Height Student Parent Student Parent 70 65 63 62 71 71 65 65 61 60 73 70 63 65 68 64 65 67 72 70 68 66 71 69 70 72 68 65 63 63 69 68 65 64