Explanation Given info: Claim : p 1 = p 2 , α = 0.10 , x 1 = 42 , n 1 = 150 , x 2 = 76 , and n 2 = 200 Justification: The value of p ¯ is, p ¯ = x 1 + x 2 n 1 + n 2 = 42 + 76 150 + 200 = 118 350 = 0.34 The value of q ¯ is, q ¯ = 1 − p ¯ = 1 − 0.34 = 0.66 The value of n 1 p ¯ is, n 1 p ¯ = 150 ( 0.34 ) = 51 The value of n 1 q ¯ is, n 1 q ¯ = 150 ( 0.66 ) = 99 The value of n 2 p ¯ is, n 2 p ¯ = 200 ( 0.34 ) = 68 The value of n 2 q ¯ is, n 2 q ¯ = 200 ( 0.66 ) = 132 The conditions are necessary in order to use the z -test to test the difference between two population proportions are given below: The samples are independent and randomly selected from the population

7th Edition

ISBN: 9780135901021

Author: Larson

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 8.4, Problem 5E

To determine

To check: Whether a normal sampling distribution can be used or not.

To test: Whether there is no difference between two population proportions or not if the normal sampling distribution can be used.

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Chapter 8.4, Problem 4E

Chapter 8.4, Problem 6E

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To check: Whether a normal sampling distribution can be used or not. To test: Whether there is no difference between two population proportions or not if the normal sampling distribution can be used.

Solution Summary: The author evaluates whether a normal sampling distribution can be used, and concludes that there is sufficient evidence to support the claim.