Persons having Raynaud'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 = 9 subjects with the syndrome, the average heat output was x = 0.61, and for n = 9 nonsufferers, the average output was 2.07. Let ₁ and ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ₁ = 0.1 and ₂ = 0.5. (a) Consider testing Ho: H₁ H₂ = -1.0 versus H₂: ₁-₂ < -1.0 at level 0.01. Describe in words what H₂ says, and then carry out the test. OH, says that the average heat output for sufferers is the same as that of non-sufferers. OH, says that the average heat output for sufferers is less than 1 cal/cm²/min below that of non-sufferers. ⒸH, says that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-sufferers. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = -5.271 X x P-value = .0010 State the conclusion in the problem context. O Fail to reject Ho. The data suggests that the average heat output for sufferers is less than 1 cal/cm²/min below that of non-sufferers. O Fail to reject Ho. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. O Reject Ho. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-sufferers. (b) What is the probability of a type II error when the actual difference between ₁ and ₂ is ₁-₂=-1.1? (Round your answer to four decimal places.) X 974 (c) Assuming that m = n, what sample sizes are required to ensure that ß = 0.1 when ₁ - ₂ = -1.1? (Round your answer up to the nearest whole number.) subjects