Answer to Question #234889 in Statistics and Probability for Steve

Question

)Suppose a production facility purchases a particular component part in large lots from a supplier. The production manager wants to estimate the proportion of defective parts received from this supplier. She believes the proportion defective is no more than .20 and wants to be within .02 of the true proportion of defective parts with a 90% level of confidence. How large a sample should she take? 

Answer 1

Sample size when estimating $p$

$$n\geq\dfrac{z^2p(1-p)}{E^2}$$

where

$p =$ population proportion

$E =$ error of estimation

$n =$ sample size

The critical value for $\alpha=0.1$ is $z_c=z_{1-\alpha/2}=1.6449.$

Given $p=0.2, E=0.02$

Substitute

$$n\geq\dfrac{(1.6449)^2(0.2)(1-0.2)}{(0.02)^2}$$

$$n=1083$$