Persons having Reynaud’s syndrome are apt to suffer a sudden impairment of blood circula...

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 = 10subjects with the syndrome, the average heat output was , and for n = 10 non sufferers, the average output was 2.05. Let μ₁ and μ₂ denote the true average heat outputs for the two types of subjects. Assume that the two distributions of heat output are normal with σ₁ = .2 and σ₂ = .4

a. Consider testing H₀: μ₁ – μ₂ =1.0 versus Ha: μ₁ – μ₂ < – 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 μ₁ and μ₂ is μ₁ – μ₂ = –1.2?

d. Assuming that m = n, what sample sizes are required to ensure that β = .1 when μ₁ – μ₂ = –1.2?