Persons having Reynauds syndrome are apt to suffer a

Chapter 9, Problem 9.5

(choose chapter or problem)

Persons having Reynauds 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? 6. An experim