Explanation Calculation: Three polls were conducted before statewide election for U.S. Senate. Of 1,500 voters, 780 were founded to favor candidate Martinez in the first poll. Of 2,500 voters, 1,285 were founded to favor candidate Martinez in the second poll. Of 3,500 voters, 1,802 were founded to favor candidate Martinez in the third poll. First poll: It is given that the sample size n = 1 , 500 and the number of voters who favor candidate Martinez are 780. Denote x as and the number of voters who favor candidate Martinez. The sample proportion is: Substituting the corresponding values to get the sample proportion, p ^ = x n = 780 1 , 500 ≈ 0.52 . Thus, the sample proportion is 0.52. Margin of error: The margin of error for the estimate of population proportion, p ^ for 95% confidence interval is, E = 1.96 × p ^ ( 1 − p ^ ) n , Where, n be the sample size, E be the margin of error and p ^ be the sample proportion. Substitute the corresponding values to get the margin of error, E = 1.96 × 0.52 ( 1 − 0.52 ) 1 , 500 = 1.96 × 0.52 ( 0.48 ) 1 , 500 = 1.96 × 0.2496 1 , 500 = 1.96 × 0.0001664 = 1.96 × 0.0129 ≈ 0.0253 Thus, the margin of error is 0.0253. The 95% confidence interval for the first poll is: 95 % CI = p ^ ± E , Where, E be the margin of error and p ^ be the sample proportion. Substitute the corresponding values to get confidence interval, p ^ ± E = 0.52 ± 0.025 = ( 0.52 − 0.025 , 0.52 + 0.025 ) ≈ ( 0.495 , 0.545 ) Thus, the 95% confidence interval for the first poll is ( 0.495 < p < 0.545 ) _ . Second poll: It is given that the sample size n = 2 , 500 and the number of voters who favor candidate Martinez is 780. Denote x as and the number of voters who favor candidate Martinez. The sample proportion is: Substituting the corresponding values to get the sample proportion, p ^ = x n = 1 , 285 2 , 500 ≈ 0.514 . Thus, the sample proportion is 0.514. Margin of error: Substitute the corresponding values to get the margin of error, E = 1.96 × 0

Statistical Reasoning for Everyday Life Plus MyLab Statistics with Pearson eText -- 18 Week Access Card Package (5th Edition)

5th Edition

ISBN: 9780135990278

Author: Bennett, Jeffrey O., Briggs, William L., Triola, Mario F.

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 8.3, Problem 29E

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Obtain the 95% confidence interval for all the three polls.

Explain the prospects for victory of Martinez based on these polls.

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Chapter 8.3, Problem 28E

Chapter 8.3, Problem 30E

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Statistical Reasoning for Everyday Life Plus MyLab Statistics with Pearson eText -- 18 Week Access Card Package (5th Edition)

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Obtain the 95% confidence interval for all the three polls. Explain the prospects for victory of Martinez based on these polls.

Solution Summary: The author explains the 95% confidence interval for all three polls and the prospects for victory of Martinez based on them.