A researcher wishes to estimate, with 99% confidence, the percentage of adults w

Question

A researcher wishes to estimate, with 99% confidence, the percentage of adults who support abolishing the penny. His estimate must be accurate within 3% of the true proportion. a) Find the minimum sample size needed, using a prior study that found that 26% of the respondents said they support abolishing the penny. b) No preliminary estimate is available. Find the minimum sample size needed. a) What is the minimum sample size needed using a prior study that found that 26% of the respondents said they support abolishing the penny? N = (Round up to the nearest whole number as needed.)

Explanation / Answer

For 99% CI, z-value = 2.58
(A)
ME = z*sqrt(p*(1-p)/n)
0.03 = 2.58 * sqrt(0.26*(1-0.26)/n)
n = (2.58/0.03)^2 * 0.26*(1-0.26) = 1422.9904

Hence 1423 should be the sample size.

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