Question

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 10 subjects with the syndrome, the average heat output was x = 0.61 and for n 10 nonsufferers, the average output was 2.04. Let μι and L2 denote the true average heat outputs for the sufferers and non sufferers, respectively. As sunne hat the two distributions of eat output are no ma with J1 0.2 and σ2° 0.4 (a) Consider testing Ho: μ1-12-1.0 versus Ha. μ1-12 <-1.0 at level Ο.Ο. Describe in words what Ha says, and then carry out the test. Ha says that the average heat output for sufferers is more than 1 cal/cm2/min below that of non-sufferers Ha says that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers. Ha 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.) P-value State the conclusion in the problem context. Reject Ho- The data suggests that the average heat output for sufferers is the same as that of non-sufferers. Fail to reject Ho. The data suggests that the average heat output for sufferers is less than 1 cal/cm*/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 (b) what is the probability of a type II error when the actual difference between μ1 and μ2 is μι-μ2--1.3? (Round your answer to four decimal places.) (c) Assuming that m-n, what sample sizes are required to ensure that β-0.1 when μι-μ2--1.37 (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.

Answer 1