Answer to Question #183724 in Statistics and Probability for Agbaohwo OFEJIRO Marvellous

Question

A key component of an electronic system is produced continuously in large numbers on a manufacturing line. When the lathe are correctly adjusted, extensive data show that the proportion of poor quality products components is 0.027. If the proportion of poor quality products in a sample of size 50 is so large that the result is significant at the 5% level, the production line will be stopped for adjustment. What is the smallest proportion of defective items in a sample of 50 that will stop the production line?

Answer 1

$p=0.027,n=50, \alpha=0.05$

$Z_{\frac{\alpha}{2}}=Z_{0.025}=1.96$

Proportion of sample that will stopped the production line is-

$\hat{p}=p+Z_{\frac{\alpha}{2}}\sqrt{\dfrac{p(1-p)}{n}}$

$=0.027+1.96\sqrt{\dfrac{0.027\times 0.973}{50}}$

$=0.027+0.04492=0.07192$

Hence The sample proportion of defective items that will stop production line is 0.07192.