For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, a is the level of significance, p̂ is the sample proportion, and n is the sample size. If it can be used, test the claim. Claim: p > 0.55; a = 0.08. Sample statistics: p̂ = 0.60, n = 150. Let q = 1 - p and let q̂ = 1 - p̂. A normal sampling distribution (can or cannot) be used here, since (np̂ or np) is (< or ≥) 5 and (nq̂ or nq) is (< or ≥) 5. a) If a normal sampling distribution can be used, identify the hypotheses for testing the claim. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. H0: p ___ 0.55 , Ha: p _ 0.55. b) If a normal sampling distribution can be used, identify the critical value(s) for this test. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. z0 = _. c) If a normal sampling distribution can be used, identify the rejection region(s). Select the correct choice below and, if necessary, fill in the answer blank(s) to complete your choice. The rejection region is z _ _. d) If a normal sampling distribution can be used, identify standardized test statistic z. z = ____. e) If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, a is the level of significance, p̂ is the sample proportion, and n is the sample size. If it can be used, test the claim.

Claim: p > 0.55; a = 0.08. Sample statistics: p̂ = 0.60, n = 150.

Let q = 1 - p and let q̂ = 1 - p̂. A normal sampling distribution (can or cannot) be used here, since (np̂ or np) is (< or ≥) 5 and (nq̂ or nq) is (< or ≥) 5.

a) If a normal sampling distribution can be used, identify the hypotheses for testing the claim. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
H0: p _______ 0.55 , Ha: p _______ 0.55.

b) If a normal sampling distribution can be used, identify the critical value(s) for this test. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. z0 = _______.

c) If a normal sampling distribution can be used, identify the rejection region(s). Select the correct choice below and, if necessary, fill in the answer blank(s) to complete your choice. The rejection region is z _______ _______.

d) If a normal sampling distribution can be used, identify standardized test statistic z.

z = ________.

e) If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision.

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