Question

What sample size is needed to give a margin of error within plus-or-minus 5% in estimating a population proportion with 90% confidence? Use z-values rounded to three decimal places. Round your answer up to the nearest integer. sample sizeequals the absolute tolerance is +/-5

Answer 1

Answer: 271.

Step-by-step explanation:

When the prior population proportion of success is not available, then the formula to find the sample size is given by :-

$n=00.25(\dfrac{z_{\alpha/2}}{E})^2$

Given : Significance level : $\alpha: 1-0.90=0.1$

By using the standard normal distribution table ,

Critical value : $z_{\alpha/2}=1.645$

Margin of error : $E=0.05$

Then , the required minimum sample size will be :-

$n=0.25(\dfrac{(1.645)}{0.05})^2=270.6025\approx271$

Hence, the required minimum sample size is 271.