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 A and all of the taller twins in set B . Create the numbers such that a two-sample t -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 -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 - and p-values for the tests. Explain why the paired t -test shows a difference and the two-sample t -test does not show a difference. Remember that 5 feet is 60 inches and that 6 feet is 72 inches.
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 A and all of the taller twins in set B . Create the numbers such that a two-sample t -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 -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 - and p-values for the tests. Explain why the paired t -test shows a difference and the two-sample t -test does not show a difference. Remember that 5 feet is 60 inches and that 6 feet is 72 inches.
Solution Summary: The author demonstrates how to construct a paired data set of heights of twins.
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
A
and all of the taller twins in set
B
. Create the numbers such that a two-sample
t
-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
-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
-
and
p-values
for the tests. Explain why the paired
t
-test
shows a difference and the two-sample
t
-test
does not show a difference. Remember that
5
feet is
60
inches and that
6
feet is
72
inches.
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