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?
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?
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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