Question

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the Social Security system. The president wants the estimate to be within 0.028 of the true proportion. Assume a 99 percent level of confidence. The president's political advisers estimated the proportion supporting the current policy to be 0.62

(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 that support current policy?

Answer 1

(a)Formula to find sample size:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is found using a z-table for 99% confidence, p = 0.62, q = 1 - p, ^2 means squared, * means to multiply, and E = 0.028.

Plug values into the formula and calculate n.

(b) Use p = 0.5 and q = 0.5
Recalculate.

I hope this will help get you started.