An article in The American Statistician 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. find out 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.