Question

a) An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 177 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

Solution :

Given that,

n = 356

x = 177

Point estimate = sample proportion = = x / n = 177/356=0.497

1 - = 0.503

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )   

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

= 1.96 (((0.497*0.503) / 356)

= 0.052

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.497-0.052 < p < 0.497+0.052

(0.445 ,0.549)