Question

Find the smallest required sample size for the following problem. Assume p (with caret) is unknown.

A manufacturer of kitchen utensils wishes to estimate the proportion of left handed people in the population.  Obtain a sample size that will ensure a margin of error of at most 0.05 for a 99​% confidence interval estimate of the proportion of left handed people in the population.

n=______ ​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

= 1 - = 0.5

margin of error = E = 0.05

Z/2 = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.05)2 * 0.5 * 0.5

= 664

sample size = 664