Question

When designing a study to determine this population proportion, what is the minimum number you would need to survey to be $90\%$ confident that the population proportion is estimated to within $0.05$ ?

Short answer

The sample size is$n=271$.

Step-by-step solution

Given Information

The confident level is $90\%$and the error estimating is$0.05$.

Explanation

The sample size is

$n={\left(\frac{z_{\frac{\alpha }{2}}}{EBP}\right)}^{2}p(1-p)$

The confident level is $90\%$,

$\frac{\alpha }{2}=\frac{1-0.90}{2}=0.05$

$z_{\frac{\alpha }{2}}=1.645$

The estimated proportion is $q=1-p$,

Both are equal to $0.5$because $pq=0.5*0.5=0.25$

$n={\left(\frac{1.645}{0.05}\right)}^{2}0.25$

$n=271$