ersons 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.
ersons 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.
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/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.
Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
State the conclusion in the problem context.
(b) What is the probability of a type II error when the actual difference between ?1 and ?2 is
(c) Assuming that m = n, what sample sizes are required to ensure that ? = 0.1 when
subjects
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 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 = | |
| P-value = |
State the conclusion in the problem context.
Fail to reject H0. The data suggests that the average heat output for sufferers is the same as that of non-sufferers.Reject H0. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. Reject H0. 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 H0. The data suggests that the average heat output for sufferers is less 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 ?1 and ?2 is
?1 − ?2 = −1.2?
(Round your answer to four decimal places.)(c) Assuming that m = n, what sample sizes are required to ensure that ? = 0.1 when
?1 − ?2 = −1.2?
(Round your answer up to the nearest whole number.)subjects
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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