Persons having Reynaud’s syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output

(cal/cm2

/min) was measured. For m
10 subjects with the syndrome, the average heat output was x
.64, and for n
10 nonsufferers, the average output was 2.05. Let 1 and 2 denote the true average heat outputs for the two types of subjects. Assume that the two distributions of heat output are normal with 1
.2 and 2
.4.

a. Consider testing H0: 1  2
1.0 versus Ha: 1 

2  1.0 at level .01. Describe in words what Ha says, and then carry out the test.

b. Compute the P-value for the value of Z obtained in part (a).

c. What is the probability of a type II error when the actual difference between 1 and 2 is 1  2
1.2?

d. Assuming that m
n, what sample sizes are required to ensure that

.1 when 1  2
1.2?