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
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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
Related questions
Question
![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 H₁ 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.
(a) State what is meant by Type I and Type II errors in this context.
(b) Find the value of a, the level of the test, if k = 6.
(c) For a = 0.05, what should be the value of k if the rejection region of the test is
{y <k}?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17176ae9-b253-442d-89f9-517b049b4c59%2F8ab0caee-619a-4214-8084-5425485e4f42%2Fuypyif_processed.png&w=3840&q=75)
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 H₁ 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.
(a) State what is meant by Type I and Type II errors in this context.
(b) Find the value of a, the level of the test, if k = 6.
(c) For a = 0.05, what should be the value of k if the rejection region of the test is
{y <k}?
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Follow-up Question
![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 H₁ 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.
(a) State what is meant by Type I and Type II errors in this context.
(b) Find the value of a, the level of the test, if k = 6.
(c) For a = 0.05, what should be the value of k if the rejection region of the test is
{y <k}?](https://content.bartleby.com/qna-images/question/17176ae9-b253-442d-89f9-517b049b4c59/82125b9e-3175-4d27-99e4-43ba8a8802cd/fygzaf_thumbnail.png)
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 H₁ 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.
(a) State what is meant by Type I and Type II errors in this context.
(b) Find the value of a, the level of the test, if k = 6.
(c) For a = 0.05, what should be the value of k if the rejection region of the test is
{y <k}?
![(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.]](https://content.bartleby.com/qna-images/question/17176ae9-b253-442d-89f9-517b049b4c59/82125b9e-3175-4d27-99e4-43ba8a8802cd/0pjfmr_thumbnail.png)
Transcribed Image Text:(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.]
Solution
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