Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an

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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 1 (92.05 KiB) Viewed 94 times

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 2.06. 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 0₁ = 0.1 and ₂ = 0.5. (a) Consider testing Ho: #₁ #₂ = -1.0 versus H₂: #₁ - #₂ < -1.0 at level 0.01. Describe in words what He says, and then carry out the test. OH says that the average heat output for sufferers is less than cal/cm²/min below that of non-sufferers. OH says that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-sufferers. OH₂ says that the average heat output for sufferers is the same as 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 = -2.39 P-value=0.0085 State the conclusion in the problem context. O Reject Ho. The data suggests that the average heat output for sufferers the same as that of non-sufferers. O Fail to reject Ho. The data suggests that the average heat output for sufferers is less than 1 cal/cm2/min below that 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. ● Reject Ho. The data suggests that the average heat output for sufferers more than 1 cal/cm2/min below that non-sufferers. (b) What is the probability of a type II error when the actual difference between ₁ and ₂ is μ₁ − #₂ = -1.4? (Round your answer to four decimal places.) X (c). Assuming that m = n, what sample sizes are required to ensure that = 0.1 when #₁ - #₂ = -1.4? (Round your answer up to the nearest whole number.) subjects