10.21
Use the data given and a 1% level of significance to test the following hypotheses. Assume the differences are normally distributed in the population.
H0: D = 0
Ha: D > 0
Pair |
Sample 1 |
Sample 2 |
1 |
38 |
22 |
2 |
27 |
28 |
3 |
30 |
21 |
4 |
41 |
38 |
5 |
36 |
38 |
6 |
38 |
26 |
7 |
33 |
19 |
8 |
35 |
31 |
9 |
44 |
35 |
Using:
With a one-tailed test, α = .01, , from table A.6.
If the observed test statistic, is greater than , the null hypothesis will be rejected.
Pair |
Sample 1 |
Sample 2 |
d |
1 |
38 |
22 |
16 |
2 |
27 |
28 |
-1 |
3 |
30 |
21 |
9 |
4 |
41 |
38 |
3 |
5 |
36 |
38 |
-2 |
6 |
38 |
26 |
12 |
7 |
33 |
19 |
14 |
8 |
35 |
31 |
4 |
9 |
44 |
35 |
9 |
∑d = 64, 7.11, 6.45, α = .01, df = 9 – 1 = 8
= 3.31 is greater than =2.90, therefore the null hypothesis will be REJECTED.