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/cm?/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 2.06. Let u, and u, 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 o, = 0.5What is the probability of a type II error vhen the actual difference between u, and uz is u, - uz = -1.1? (Round your answer to four decimal places.)Assuming that m = n, what sample sizes are required to ensure that B = 0.1 when u1 - H2 = -1.1? (Round your answer up to the nearest whole number.)

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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.EA: Extended Application Flow Systems

Problem 2EA

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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/cm?/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 2.06. Let u, and uz 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 oz = 0.5. vA, says tnal ule a y---- 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 = What is the probability of a type II error when the actual difference between u, and uz is u - uz = -1.1? (Round your answer to four decimal places.) Assuming that m = n, what sample sizes are required to ensure that 8 = 0.1 when u - uz…
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 = 0.63, and for n = 9 nonsufferers, the average output was 2.07. Let ₁ and ₂ 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: H₁ H₂ = -1.0 versus H₂: H₁ H₂ < -1.0 at level 0.01. Describe in words what H₂ 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. Ⓒ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…
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 = 0.61, and for n = 9 nonsufferers, the average output was 2.09. Let ?1 and ?2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with ?1 = 0.3 and ?2 = 0.5. (a) Consider testing H0: ?1 − ?2 = −1.0 versus Ha: ?1 − ?2 < −1.0 at level 0.01. Describe in words what Ha says, and then carry out the test. Ha says that the average heat output for sufferers is the same as 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 more…
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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 2.06. Let µj and µɔ denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with o1 = 0.1 and 02 = 0.5. (a) Consider testing Ho: H1 - H2 = -1.0 versus Ha: µ1 - 42 < -1.0 at level 0.01. Describe in words what Ha says, and then carry out the test. Ha says that the average heat output for sufferers is the same as that of non-sufferers. 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…
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