Suppose the U.S. President wants an estimate of the proportion of the population

Question

Suppose the U.S. President wants an estimate of the proportion of the population who support his current policy towards revisions in the Social Security system. The president wants the estimate to be with .04 of the true proportion. Assume a 95% level of confidence. The president’s political advisors estimate the proportion supporting the current policy to be 60.

a. How large of a sample is required?
b. How large of a sample would be necessary if no estimate were available for the proportion supporting current policy?

Explanation / Answer

a. the formula is n = [z*/ME]^2 (pq); we know that z* = 1.96 for 95% confidence, we want ME = 0.04, and we estimate p = 0.60, so q = 0.40. Thus: n = [1.96/.04]^2 (0.60*0.40) = 576 b. If we have no estimate for p, then we use p = 0.50, so q = 0.50: n = [1.96/.04]^2 (0.50*0.50) = 600

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