A sports physiologist wants to know if people have
the same strength in each arm. He takes
data from 12 people, measuring strength using a nifty machine with units that
aren’t important.
|
Person |
Right |
Left |
|
1 |
16 |
12 |
|
2 |
12 |
15 |
|
3 |
8 |
9 |
|
4 |
11 |
15 |
|
5 |
9 |
9 |
|
6 |
29 |
25 |
|
7 |
21 |
18 |
|
8 |
18 |
16 |
|
9 |
16 |
18 |
|
10 |
13 |
11 |
|
11 |
14 |
12 |
|
12 |
25 |
20 |
At the 10% significance level, test whether or not
strength in the right arm is the same as that in the left for these
people. Use the parametric test.
Can
you think of what might have been a better null hypothesis?
Answers:
d(bar) = 1, s(d-bar) = 0.85, t(obs) = 1.173, 0.20 < p < 0.50
A better hypothesis might have been that the dominant arm is stronger. That is, right-handed people have stronger right arms, and left-handed people have stronger left arms. (How would you set this up as a one-sided hypothesis test?)