a. Explanation Given info: In a Pew Research, 57% out of 2,254 U.S adults said that they favoured marriage equality when they were asked whether they strongly favour, favour, oppose, or strongly oppose allowing gays and lesbians to marry legally. Calculation: Sampling distribution of a sample proportion: For all possible samples the distribution of proportion is called the sampling distribution of proportion Conditions: Randomization condition: Sample should be a random sample. 10% condition: The sample drawn should be less than 10% of the population. Success/Failure Condition: both n p ^ and n q ^ should be greater than or equal to 10. Here the sample of 2,254 adults is drawn at random. 10% condition: Here 2,254 is less than the 10% of all U.S adults. The sample drawn is less than 10% of the population. Success/Failure Condition: Substitute n as 2,254 and p ^ as 0.57, n p ^ = 2 , 254 ( 0.57 ) = 1 , 284.78 ≈ 1 , 285 > 10 Substitute n as 2,254 and q ^ as 0 b. To determine Explain whether it can be concluded that the majority of U.S. adults support legally recognizing gay marriages based on the confidence interval or not. c. To determine Find the number of people to be polled.

Intro Stats, Books a la Carte Edition (5th Edition)

5th Edition

ISBN: 9780134210285

Author: Richard D. De Veaux, Paul Velleman, David E. Bock

Publisher: PEARSON

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Chapter R, Problem 4.19RE

To determine

Obtain a 95% confidence interval.

To determine

Explain whether it can be concluded that the majority of U.S. adults support legally recognizing gay marriages based on the confidence interval or not.

To determine

Find the number of people to be polled.

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Chapter R, Problem 4.18RE

Chapter R, Problem 4.20RE

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Obtain a 95% confidence interval.

Solution Summary: The author explains how to obtain a 95% confidence interval using MINTAB software.

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Obtain a 95% confidence interval.

Explain whether it can be concluded that the majority of U.S. adults support legally recognizing gay marriages based on the confidence interval or not.

Find the number of people to be polled.

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Chapter R Solutions