Please answer all questions9 and show all work 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 aforefinger 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, theaverage output was 2.07. Let μ₁ and μ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with0₁ = 0.1 and ₂ = 0.5.(a) Consider testing Ho: M₁ M₂ = -1.0 versus H₂: M₁-M₂ < -1.0 at level 0.01. Describe in words what H₂ says, and then carry out the test.O H₂ says that the average heat output for sufferers is the same as that of non-sufferers.O H₂ says that the average heat output for sufferers is less than 1 cal/cm²/min below that of non-sufferers.ⒸH₂ 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 = -5.271XXP-value .0010State 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 μ₁ and μ₂ is μ₁ −μ₂ = -1.1? (Round your answer to four decimal places.).974X(c) Assuming that m = n, what sample sizes are required to ensure that ß = 0.1 when μ₁ - ₂ = -1.1? (Round your answer up to the nearest whole number.)subjects

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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