The data in the table below is a random sample of 15 observations each from two normal populations with unknown means and variances. Test the null hypothesis that the two population means are equal against the alternative that μY > μX . First assume that the two population variances are equal. Interpret your results. Repeat the test without assuming equal variances. Is there a difference in the conclusions?
|
Sample 1
|
X
12.03
|
Y
13.74
|
|
2
|
13.01
|
13.59
|
|
3
|
9.75
|
10.75
|
|
4
|
11.03
|
12.95
|
|
5
|
5.81
|
7.12
|
|
6
|
9.28
|
11.38
|
|
7
|
7.63
|
8.69
|
|
8
|
5.70
|
6.39
|
|
9
|
11.75
|
12.01
|
|
10
|
6.28
|
7.15
|
|
11
|
12.53
|
13.47
|
|
12
|
10.22
|
11.57
|
|
13
|
7.17
|
8.81
|
|
14
|
11.36
|
13.10
|
|
15
|
9.16
|
11.32
|