A simple random sample of size 400 was taken from the popula

A simple random sample of size 400 was taken from the population of all manufacturing establishments in a certain stare: 11 establishments in the sample had 100 employees of more. Estimate the percentage of manufacturing establishments with 100 employees or more and attach a standard error to the estimation.

Solution

Given, sample size n=400

Estimated proportion of establishments with 100 or more employees = p= 11/400 = 2.75%

Standard error = sqrt(p*(1-p)/n) = sqrt(.0275*.975/400) = 0.0082 = 0.818%