Question

What is the minimum sample size needed to estimate a population proportion to within 5% with 98% confidence? Assume that there is no prior knowledge of the true value of the proportion, and enter your answer as a whole number.

Answer 1

Answer: 543

Explanation:

When we have no prior knowledge of the true value of the proportion, then the formula to find the minimum sample size is given by :-

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

Given : Margin of error : E = 0.05

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

By standard normal distribution table , the critical value will be :-

`z_(\alpha/2)=z_(0.01)=2.33`

Then,
`n=0.25((2.33)/(0.05))^2=542.89\approx543`

Hence, the minimum sample size needed to estimate a population proportion = 543