After calculating the sample size needed to estimate a population proportion to within 0.04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led to a sample size of 800, the sample size will now have to be:
A) 800
B) 3200
C) 12,800
D) 6400
E) 1600

Question

Quizplus · Accepted Answer

The sample size needed to estimate a population proportion with a certain level of confidence is inversely proportional to the square of the allowable error. If the allowable error decreases from 0.04 to 0.01, the square of the ratio of the original error to the new error is (0.04/0.01)^2 = 16. Therefore, the new sample size is 16 times the original sample size: 800 * 16 = 12,800.

After Calculating the Sample Size Needed to Estimate a Population