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/cm/min) was measured. For m = 10 subjects with the syndrome, the average heat output was = .64, and for n = 10 nonsufferers, the average output was 2.05. Let and 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 02 = .4. a. Consider testing Ho = -1.0 versus Ha- 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?