A pharmaceutical company claims 90% success rate of a newly invented drug to treat arthritis pain. To examine the claim, a doctor administered the prescribed dose to 10 arthritis patients. She observed Y, the number of participants for which the drug was effective. A test is defined so as to reject Ho: p= 0.9 in favour of H.: P < 0.9 by the rejection region {y

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A pharmaceutical company claims 90% success rate of a newly invented drug to treat
arthritis pain. To examine the claim, a doctor administered the prescribed dose to 10
arthritis patients. She observed Y, the number of participants for which the drug was
effective. A test is defined so as to reject Ho: p = 0.9 in favour of Ha: p < 0.9 by
the rejection region {y < k} where k is a positive integer. Note that p is the population
proportion of arthritis patients for which the drug was effective.
(d) Find the power of the test for p = 0.3, 0.5, 0.7, 0.9.
(e) Sketch a graph of the power function against p (0 < p ≤ 1), and comment on how
the power changes as p changes. [Hint: You may use Table 1 in Appendix 3 of
WMS.]
Transcribed Image Text:A pharmaceutical company claims 90% success rate of a newly invented drug to treat arthritis pain. To examine the claim, a doctor administered the prescribed dose to 10 arthritis patients. She observed Y, the number of participants for which the drug was effective. A test is defined so as to reject Ho: p = 0.9 in favour of Ha: p < 0.9 by the rejection region {y < k} where k is a positive integer. Note that p is the population proportion of arthritis patients for which the drug was effective. (d) Find the power of the test for p = 0.3, 0.5, 0.7, 0.9. (e) Sketch a graph of the power function against p (0 < p ≤ 1), and comment on how the power changes as p changes. [Hint: You may use Table 1 in Appendix 3 of WMS.]
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Step 1: To find the power of the test.

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