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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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

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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 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}?

(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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