Question

A quality control engineer wants to determine what proportion of defective parts are coming off the assembly line. What sample size does the engineer need in order to estimate the true proportion within a margin of error (maximum bound on the error) of 0.12 with 90% confidence?

Answer 1

Answer: 47

Step-by-step explanation:

Given : Margin of error : $E=0.12$

Significance level : $\alpha: 1-0.90=0.10$

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

The formula to find the sample size when no prior proportion exists is given by :-

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2$

i.e. $n=0.25(\dfrac{1.645}{0.12})^2$

$=46.9796006944\approx47$

Hence, the minimum required sample size =47