Question

An eCommerce website displays the content slightly differently depending on the device used to access the website. Suppose the website manager knows that the proportion of customers who access the website using a smartphone is 0.58. The website manager wants to collect a sample such that the standard deviation of the sample proportion is less than 0.04. What is the minimum sample size required to satisfy this criterion?

Answer 1

Given that, sample proportion \((\hat{p})=0.58\)

standard deviation (SE) of the sample proportion is 0.04

We want to find the sample size (n),

\(S E=\sqrt{\frac{\hat{p} *(1-\hat{p})}{n}}\)

\(=>n=\frac{\hat{p} *(1-\hat{p})}{(S E)^{2}}\)

\(=>n=\frac{0.58 *(1-0.58)}{(0.04)^{2}}\)

\(=>n=152.25\)

\(=>n \approx 152\)

Therefore, required sample size is 152