Question

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 210 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.

Answer 1

95% (two-sided) confidence interval for the proportion of all dies that pass the probe is 0.590±0.051 (between 0.539 and 0.641)

Explanation:

Confidence Interval can be calculated using p±ME where

• p is the samle proportion of dies that pass the probe (
  `(210)/(356)` =0.590)
• ME is the margin of error from the mean

and margin of error (ME) around the mean can be found using the formula

ME=
`(z*√(p*(1-p)))/(√(N) )` where

• z is the statistic in 95% confidence level (1.96)

• p is the sample proportion (
  `(210)/(356)=0.590`

• N is the sample size (356)

Then ME=
`(1.96*√(0.59*0.41))/(√(356) )`=0.051

95% confidence interval is 0.590±0.051