Question

Suppose a company wants to determine the current percentage of customers who are subjected to their advertisements online. How many customers should the company survey in order to be 98% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are subjected to their advertisements online? z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576

Answer 1

Answer: 1503

Explanation:

Given : Significance level :
`\alpha:1-0.98=0.02`

Critical value :
`z_(\alpha/2)=2.326`

Margin of error :
`E=\pm0.03`

We know that the formula to find the sample size (the prior true proportion is not available) is given by :-

`n=0.25((z_(\alpha/2))/(E))^2`

i.e.
`n=0.25((2.326)/(0.03))^2=1502.85444444\approx1503`

Hence, the minimum sample size should be 1503.