Chapter 9, Problem 100CRE

Construct heights for 3 or more sets of twins (6 or more people). Make the twins similar, but not exactly the same, in height. Put all of the shorter twins in set $\text{A}$ and all of the taller twins in set $\text{B}$. Create the numbers such that a two-sample $t\text{-test}$ will not show a significant difference in the mean heights of the shortest of each pair, and the mean heights of the tallest of each pair, but the paired $t\text{-test}$ does show a significant difference. (Hint: Make one of the pairs really tall, one of the pairs really short, and one of the pairs in between.) Report all the numbers and the $t\text{-}$ and $\text{p-values}$ for the tests. Explain why the paired $t\text{-test}$ shows a difference and the two-sample $t\text{-test}$ does not show a difference. Remember that $5$ feet is $60$ inches and that $6$ feet is $72$ inches.