There are two candidates in a presidential election: Candidate A and Candidate B. Let be the

There are two candidates in a presidential election: Candidate A and Candidate B. Let θ be the portion of people who plan to vote for Candidate A. Our goal is to find a confidence interval for θ. Specifically, we choose a random sample (with replacement) of n voters and ask them if they plan to vote for Candidate A. Our goal is to estimate the θ such that the margin of error is 3 percentage points. Assume a 95% confidence level. That is, we would like to choose n such that

where X̅ is the portion of people in our random sample that say they plan to vote for Candidate A. How large does n need to be?

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P(X X-0.03 ≤0 ≤X +0.03) ≥ 0.95,