Question

. A quality controller wants to estimate the proportion of high quality goods out of a batch of products with a 90% confidence level and a margin of error of 5%. How many products must he test. 30

Answer 1

A 90% confidence interval has a z-score (a critical value) $z_c=1.6449.$

$$ME=z_c\times\sqrt{\dfrac{p(1-p)}{n}}$$

$$=1.6449\times\sqrt{\dfrac{0.5(1-0.5)}{n}}=0.05$$

$$n=(16.449)^2$$

$$n=271$$