A sample of components made by a factory in China shows that 6 out of a sample of 50 were found to be faulty. What is the width of a 95% confidence interval (z = 1.96) for the defect rate (2 decimal places)?
A) 0.12 ± 0.06
B) 0.12 ± 0.09
C) 0.12 ± 0.12
D) 0.12 ± 0.15

Question

Quizplus · Accepted Answer

The defect rate (p) is 6/50 = 0.12. The standard error (SE) for the proportion is calculated using the formula SE = sqrt[(p(1-p))/n], where n is the sample size. SE = sqrt[(0.12*0.88)/50] = 0.046. The margin of error (ME) at 95% confidence level is z*SE, where z is 1.96 for 95% confidence. ME = 1.96*0.046 = 0.09. Therefore, the width of the confidence interval is 0.12 ± 0.09.

A Sample of Components Made by a Factory in China