Given that n observations will produce a binomial parameter estimator, x/n, havi

Question

Given that n observations will produce a binomial parameter estimator, x/n, having a margin of error equal to 0.06, how many observations are required for the proportion to have a margin of error half that size? Given that a political poll shows that 52% of the sample favors Candidate A, whereas 48% would vote for Candidate B, and given that the margin of error associated with the survey is 0.05, does it make sense to claim that the two candidates are tied? Explain. Assume that the binomial parameter p is to be estimated with the function x/n, where X is the number of successes in n independent trials. Which demands the larger sample size: requiring that x/n have a 96% probability of being within 0.05 of p, or requiring that x/n have a

Explanation / Answer

3.23

Note that

E1^2 n1 = E2^2 n2

where E and n are the margins of errors and sample sizes.

Hence, as E1 = 0.06, E2 = 0.06/2 = 0.03, n1 = n,

0.06^2 n = 0.03^2 n2

n2 = 4n [ANSWER: 4n]

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