Question

1. [5/6 Points] DETAILS MY NOTES DEVORESTAT9 9.1.005.S. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER 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 = 8 subjects with the syndrome, the average heat output was x = 0.65, and for n = 8 nonsufferers, the average output was 2.09. 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 σ₁ = 0.1 and 0₂ = 0.5. You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) Consider testing Ho: μ₁ - μ₂ = -1.0 versus Η: μ₁ - μ₂ < -1.0 at level 0.01. Describe in words what He says, and then carry out the test. H₂ says that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-sufferers. OH says that the average heat output for sufferers is the same as that of non-sufferers. OH says that the average heat output for sufferers is less than 1 cal/cm²/min below that of non-sufferers. Calculate the test statistic. (Round your answer to two decimal places.) z = -2.44 Use technology to find the P-value. (Round your answer to four decimal places.) P-value = 0.0073 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. Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm²/min below that of non- sufferers. 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. Fail to 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 µ₁ and µ₂ is μ₁ - μ₂ = -1.4? (Round your answer to four decimal places.) 0.5428 (c) Assuming that m = n, what sample sizes are required to ensure that ẞ = 0.1 when μ₁ – μ₂ = -1.4? (Round your answer up to the nearest whole number.) 4 x subjects Need Help? Read It Watch It

Name: 1 56 points details my notes devorestat9 91005s previous answers ask your teacher practice another persons having raynauds syndrome are apt to suffer a sudden impairment of blood circulation 06163
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Description: 1 56 points details my notes devorestat9 91005s previous answers ask your teacher practice another persons having raynauds syndrome are apt to suffer a sudden impairment of blood circulation 06163

1. [5/6 Points]
DETAILS
MY NOTES
DEVORESTAT9 9.1.005.S.
PREVIOUS ANSWERS
ASK YOUR TEACHER
PRACTICE ANOTHER
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 = 8 subjects with the
syndrome, the average heat output was x = 0.65, and for n = 8 nonsufferers, the average output was 2.09. 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 σ₁ = 0.1 and 0₂ = 0.5.
You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question.
(a) Consider testing Ho: μ₁ - μ₂ = -1.0 versus Η: μ₁ - μ₂ < -1.0 at level 0.01. Describe in words what He says, and then carry out the test.
H₂ says that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-sufferers.
OH says that the average heat output for sufferers is the same as that of non-sufferers.
OH says that the average heat output for sufferers is less than 1 cal/cm²/min below that of non-sufferers.
Calculate the test statistic. (Round your answer to two decimal places.)
z = -2.44
Use technology to find the P-value. (Round your answer to four decimal places.)
P-value = 0.0073
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.
Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-
sufferers.
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.
Fail to 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 µ₁ and µ₂ is μ₁ - μ₂ = -1.4? (Round your answer to four decimal places.)
0.5428
(c) Assuming that m = n, what sample sizes are required to ensure that ẞ = 0.1 when μ₁ – μ₂ = -1.4? (Round your answer up to the nearest whole
number.)
4
x subjects
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