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 = 8 subjects with the syndrome, the average heat output was x = 0.63, and for n = 8 nonsufferers, the average output was 2.08. Let ₁ and ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions heat output are normal with ₁0.1 and ₂-0.5. (a) Consider testing Ho: #₁ #₂ -1.0 versus Ha: #₁ #₂ < -1.0 at level 0.01. Describe in words what H says, and then carry out the test. H 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 the same as 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 = P-value= State the conclusion in the problem context. 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. Fail to 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. Reject Ho. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. (b) What the probability of a type II error when the actual difference between ₁ and ₂ is #₁ #₂ = -1.2? (Round your answer to four decimal places.) (c) Assuming that m= n, what sample sizes are required to ensure that = 0.1 when #₁ #₂ = -1.2? (Round your answer up to the nearest whole number.) subjects