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DEVORESTAT9 9.1.005.

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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.)

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You may need to use the appropriate table in the Appendix of Tables to answer this question.

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