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 subjects with the syndrome, the average heat output was , and for nonsufferers, the average output was 2.05. Let m1 and m2 denote the true average heat outputs for the two types of subjects. Assume that the two distributions of heat output are normal with and .

a. Consider testing H0: m1 m2  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 m1 and m2 is ? m1 2 m2 5 21.2

d. Assuming that , what sample sizes are required to ensure that when ?