Question

A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 95​% confidence if ​she uses a previous estimate of 0.32​?

Answer 1

Answer: 8359

Step-by-step explanation:

The formula for sample size needed for interval estimate of population proportion :-

$n=p(1-p)(\frac{z_{\alpha/2}}{E})^2$

Given : The significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}}=z_{0.025}=\pm1.96$

Previous estimate of proportion : $p=0.32$

Margin of error : $E=0.01$

Now, the required sample size will be :-

$n=0.32(1-0.32)(\frac{1.96}{0.01})^2=8359.3216\approx8359$

Hence, the required sample size = 8359