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6. A newspaper plans to conduct a survey for the upcoming presidential election in order to estimate the proportion of the population, p, who supports a certain candidate. What is the smallest sample size needed to obtain an estimate that is within 4% of the true proportion p at the 96% confidence level?

6. A newspaper plans to conduct a survey for the upcoming presidential election in order to estimate the proportion of the population, p, who supports a certain candidate. What is the smallest sample size needed to obtain an estimate that is within 4% of the true proportion p at the 96% confidence level?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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I got this answer wrong on a practice test, and am still not sure how to correctly solve it. Could you please show me step by step?

 
6. A newspaper plans to conduct a survey for the upcoming presidential election in order to estimate the proportion of the population, p, who supports a certain candidate. What is the smallest sample size needed to obtain an estimate that is within 4% of the true proportion p at the 96% confidence level? (A) 26 (В) 376 (B) 601 (D) 660 (E) Cannot be determined from information given. Answered Wed May 19 2021 19:52:41 GMT-0700 Answer Explanation The correct answer is (D). Since we don't have an estimate for p, we use p=0.5, which gives us the largest possible margin of error, and the critical value for 96% confidence is z* = 2.054. Use algebra to solve for n and then round up to 660.
Transcribed Image Text:6. A newspaper plans to conduct a survey for the upcoming presidential election in order to estimate the proportion of the population, p, who supports a certain candidate. What is the smallest sample size needed to obtain an estimate that is within 4% of the true proportion p at the 96% confidence level? (A) 26 (В) 376 (B) 601 (D) 660 (E) Cannot be determined from information given. Answered Wed May 19 2021 19:52:41 GMT-0700 Answer Explanation The correct answer is (D). Since we don't have an estimate for p, we use p=0.5, which gives us the largest possible margin of error, and the critical value for 96% confidence is z* = 2.054. Use algebra to solve for n and then round up to 660.
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