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(b) What is the probability of a type II error when the actual difference between μ₁ and μ₂ μ₁ −μ₂ = -1.5? (Round your answer to four decimal places.) 0.1251 X (c) Assuming that m = n, what sample sizes are required to ensure that ß = 0.1 when μ₁-₂=-1.5? (Round your answer up to the nearest whole number.) subjects

(b) What is the probability of a type II error when the actual difference between μ₁ and μ₂ μ₁ −μ₂ = -1.5? (Round your answer to four decimal places.) 0.1251 X (c) Assuming that m = n, what sample sizes are required to ensure that ß = 0.1 when μ₁-₂=-1.5? (Round your answer up to the nearest whole number.) subjects

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Please answer part B and C. Thank You

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 = 9 subjects with the syndrome, the average heat output was x = 0.62, and for n = 9 nonsufferers, the average output was 2.04. Let μ₁ and μ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ₁ = 0.1 and ₂ = 0.5. (a) Consider testing Ho: M₁ M₂ = -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 1 cal/cm²/min below that of non-sufferers. O H₂ says that the average heat output for sufferers is the same as that of non-sufferers. ⒸH₂ 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.) z = -2.47 P-value = 0.0068 State the conclusion in the problem context. O Fail to reject Ho. The data suggests that the average heat output for sufferers is less than 1 cal/cm²/min below that of 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. O 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 μ₁-M₂= -1.5? (Round your answer to four decimal places.) X 0.1251 (c) Assuming that m = n, what sample sizes are required to ensure that ß = 0.1 when μ₁ −μ₂ = -1.5? (Round your answer up to the nearest whole number.) subjects
Transcribed Image Text: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 = 9 subjects with the syndrome, the average heat output was x = 0.62, and for n = 9 nonsufferers, the average output was 2.04. Let μ₁ and μ₂ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ₁ = 0.1 and ₂ = 0.5. (a) Consider testing Ho: M₁ M₂ = -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 1 cal/cm²/min below that of non-sufferers. O H₂ says that the average heat output for sufferers is the same as that of non-sufferers. ⒸH₂ 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.) z = -2.47 P-value = 0.0068 State the conclusion in the problem context. O Fail to reject Ho. The data suggests that the average heat output for sufferers is less than 1 cal/cm²/min below that of 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. O 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 μ₁-M₂= -1.5? (Round your answer to four decimal places.) X 0.1251 (c) Assuming that m = n, what sample sizes are required to ensure that ß = 0.1 when μ₁ −μ₂ = -1.5? (Round your answer up to the nearest whole number.) subjects
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