Question

2) A manufacturer wishes to estimate the proportion of washing machines leaving the factory that are defective. How large a sample should she check in order to be 90% confident that the true proportion is estimated to within 4%?

Answer 1

We have given,                  
Preliminary estimate for proportion (Not Known) = 0.5
Margin of error =E=0.04
Level of significance =1-0.90=0.1
Z critical value is (by using Z table) =1.645

$n=\left [ \hat{p} (1-\hat{p})\right ]\left [ \frac{Z}{E} \right ]^2= \left[ 0.5 * 0.5 \right]\left[\frac{ 1.645 }{ 0.04 }\right]^2= 422.82 \approx423$ Sample size =423