2- 0.5. 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 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 e,-0.1 and (a) Consider testing Họ: H1 - H2 = -1.0 versus H: H1 - #2 < -1.0 at level 0.01. Describe in words what H, 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/cm/min below that of non-sufferers. H, says that the average heat output for sufferers is less 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.) P-value = State the conclusion in the problem context. Fail to reject Hg. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. Fail to reject Hg- The data suggests that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers. Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm/min below that of non-sufferers. Reject Hn. 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 1 and az is H1 - #2 = -1.1? (Round your answer to four decimal places.) 0.1190 (c) Assuming that m = n, what sample sizes are required to ensure that p = 0.1 when 1 - #2 = -1.1? (Round your answer up to the nearest whole number.) 0.904 x subjects
2- 0.5. 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 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 e,-0.1 and (a) Consider testing Họ: H1 - H2 = -1.0 versus H: H1 - #2 < -1.0 at level 0.01. Describe in words what H, 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/cm/min below that of non-sufferers. H, says that the average heat output for sufferers is less 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.) P-value = State the conclusion in the problem context. Fail to reject Hg. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. Fail to reject Hg- The data suggests that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers. Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm/min below that of non-sufferers. Reject Hn. 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 1 and az is H1 - #2 = -1.1? (Round your answer to four decimal places.) 0.1190 (c) Assuming that m = n, what sample sizes are required to ensure that p = 0.1 when 1 - #2 = -1.1? (Round your answer up to the nearest whole number.) 0.904 x subjects
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 2.06. 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 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 Ho: The data suggests that the average heat output for sufferers is the same as that of non-sufferers.
Fail to reject Ho: The data suggests that the average heat output for sufferers is less than 1 cal/cm/min below that of non-sufferers.
o Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-sufferers.
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 u1 and uz is µ1 - H2
= -1.1? (Round your answer to four decimal places.)
0.1190
(c) Assuming that m = n, what sample sizes are required to ensure that ß = 0.1 when u1 - Hɔ = -1.1? (Round your answer up to the nearest whole number.)
0.904
x subjects
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