Question

Confidence Intervals and Minimum Sample Sizes

     Use your set of z-scores to find the following:

1. A random sample of 200 computer chips is obtained from one company and 4% are found to be defective. Find the 95% confidence interval for the proportion of chips from that factory that are not defective.

Answer 1

Given a random sample of n = 200 computer chips is obtained from one company and 4% are found to be defective so, the percentage of non-defective products will be (100-4) % = 96%, thus converting into sample proportion as:

at a 95% confidence level, the α=0.05 Zc​=Z1−α/2 ​ score is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.975), thus Zc computed as 1.96.

The confidence interval is calculated as:

Thus the proportion of chips from that factory that are not defective is {0.933, 0.987}