Question

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 186 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 between 0.470 and 0.574

Explanation:

Confidence interval can be calculated as p±ME where

• p is the sample proportion of dies that pass the probe
• ME is the margin of error

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

ME=
`(z*√(p*(1-p)))/(√(N) )` where

• z is the corresponding statistic in 95% confidence level (1.96)
• p is the sample proportion (
  `(186)/(356)=0.522`)

• N is the sample size (356)

Using the numbers in the formula we get

ME=
`(1.96*√(0.522*0.478))/(√(356) )` ≈0.052

then the 95% confidence interval would be 0.522±0.052