Find the minimum sample size you will need if you ant to be within 2% of the population proportion?

Question

A study shows that 27% of Americans say chocolate is their favorite ice cream flavor. You want to estimate, with 95% confidence, the true proportion of U>S> adults who say chocolate is their favorite ice cream flavor.

Answer 1

Margin of Error = critical value × Standard Error

We want the Margin of Error to be 2%.

We know that the population proportion p = .27

The sample variance will then be p × (1-p) = (.27 ×( 1-.27) )/n = .1971⁄n and the standard error (or sample standard deviation) will be the square root of the sample variance.

Standard error = √.1971/√n = .4440/√n

The critical value =1.96. This is z value that corresponds with a 95% confidence interval is 1.96 (Remember this means .05/2 or .025% of the normal curve is not included on each end so this means we choose the z value that the Pr(Z<z)= 97.5%

So we have .02 < 1.96 ×.4440/√n

n > 1893.29

So n = 1894 . That is my final answer