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 suddenimpairment of blood circulation in fingers and toes. In anexperiment to study the extent of this impairment, each subjectimmersed 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 2.01. Let 𝜇1 and 𝜇2 denote the true averageheat outputs for the sufferers and nonsufferers, respectively.Assume that the two distributions of heat output are normal with 𝜎1= 0.1 and 𝜎2 = 0.5. (a) Consider testing H0: 𝜇1 − 𝜇2 = −1.0 versusHa: 𝜇1 − 𝜇2 < −1.0 at level 0.01. Describe in words what Hasays, and then carry out the test. Ha says that the average heatoutput for sufferers is more than 1 cal/cm2/min below that ofnon-sufferers. Ha says that the average heat output for sufferersis less than 1 cal/cm2/min below that of non-sufferers. Ha saysthat the average heat output for sufferers is the same as that ofnon-sufferers. Correct: Your answer is correct. Calculate the teststatistic and P-value. (Round your test statistic to two decimalplaces and your P-value to four decimal places.) z = -2.91Incorrect: Your answer is incorrect. P-value = 0.0010 Incorrect:Your answer is incorrect. State the conclusion in the problemcontext. Fail to reject H0. The data suggests that the average heatoutput for sufferers is less than 1 cal/cm2/min below that ofnon-sufferers. Reject H0. The data suggests that the average heatoutput for sufferers is more than 1 cal/cm2/min below that ofnon-sufferers. Fail to reject H0. The data suggests that theaverage heat output for sufferers is the same as that ofnon-sufferers. Reject H0. The data suggests that the average heatoutput for sufferers is the same as that of non-sufferers. Correct:Your answer is correct. (b) What is the probability of a type IIerror when the actual difference between 𝜇1 and 𝜇2 is 𝜇1 − 𝜇2 =−1.3? (Round your answer to four decimal places.) (c) Assuming thatm = n, what sample sizes are required to ensure that 𝛽 = 0.1 when𝜇1 − 𝜇2 = −1.3? (Round your answer up to the nearest whole number.)subjects