Question

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 193 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.)

please show work and formulas in detail

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 193 / 356 = 0.542

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.542 * 0.558) / 356)

= 0.052

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.542 - 0.052 < p < 0.542 + 0.052

0.490 < p < 0.594

(0.490 , 0.594)