An article in The American Statistician (M. L. R. Ernst, et al., "Scatterplots for Unordered Pairs," 50 (1996), pp. 260-265) reports on the difference in the measurements by two evaluators of the cardiac output of 23 patients using Doppler echocardiography. Both observers took measurements from the same patients. The measured outcomes were as follows:
|
Patient
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
Evaluator 1
|
4.8
|
5.6
|
6
|
6.4
|
6.5
|
6.6
|
6.8
|
7
|
7
|
7.2
|
7.4
|
7.6
|
|
Evaluator 2
|
5.8
|
6.1
|
7.7
|
7.8
|
7.6
|
8.1
|
8
|
8.21
|
6.6
|
8.1
|
9.5
|
9.6
|
|
Patient
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
|
|
Evaluator 1
|
7.7
|
7.7
|
8.2
|
8.2
|
8.3
|
8.5
|
9.3
|
10.2
|
10.4
|
10.6
|
11.4
|
|
|
Evaluator 2
|
8.5
|
9.5
|
9.1
|
10
|
9.1
|
10.8
|
11.5
|
11.5
|
11.2
|
11.5
|
12
|
|
a. Conduct a hypothesis test to determine if the average cardiac outputs measured by the two evaluators differ. Use a significance level of 0.02.
b. Calculate the standard error of the difference between the two average outputs assuming that the sampling was done independently. Compare this with the standard error obtained in part a.