3. Submit Answer DEVORESTAT9 9.1.005. DETAILS Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood qrculation 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 - 0.65, and for n=8 nonsufferers, the average output was 2.01. Let #, and , denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with o,-0.1 and %₂=0.3. (a) Consider testing H₁ H₁-H₂=-1.0 versus H: ₂-₂-1.0 at level 0.01. Describe in words what H, says, and then carry out the test. OH, 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 less than 1 cal/cm³/min below that of non-sufferers. CH, 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.) 2= P-value- State the conclusion in the problem context. Fail to reject H₂. 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/cm/min below that of non-sufferers. Fail to reject H. The data suggests that the average heat output for sufferers is less 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 is the probability of a type II error when the actual difference between ₁ and ₂ is ₁-₂ -1.5? (Round your answer to four decimal places.) (c) Assuming that m-n, what sample sizes are required to ensure that = 0.1 when H₁-H₂=-1.5? (Round your answer up to the nearest whole number.) subjects You may need to use the appropriate table in the Appendix of Tables to answer this question. MY NOTES MacBook Pro