Question

1. Construct a 95% confidence interval for the proportion of defective items in a process when it is found that a random sample of 100 items contains 6 defectives.

2. How large a sample is needed in problem 1 above to estimate the proportion of defective items to within 2% with 95% confidence?

Answer 1

Solution,

Given that,

1) = 6 / 100 = 0.06

1 - = 1 - 0.06 = 0.94

2) margin of error = E = 0.02

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z_/2 = Z_0.025 = 1.96   

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96 / 0.02 )² * 0.06 * 0.94

= 541.66

sample size = n = 542