Question

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 212 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

Answer: (0.545, 0.647)

Step-by-step explanation:

Let p be the population proportion of all dies that pass the probe.

Given : An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 212 of these passed the probe.

i.e.Sample size : n= 356

Sample proportion of all dies that pass the probe: $\hat{p}=\dfrac{212}{356}\approx0.596$

Critical value for 95% confidence interval ( Using z-value table) :

$z=1.96$

Now, the 95% (two-sided) confidence interval for the proportion of all dies that pass the probe will be :

$\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

i.e. $0.596\pm (1.96)\sqrt{\dfrac{0.596(1-0.596)}{356}}$

i.e. $0.596\pm (1.96)(0.026)$

$\approx0.596\pm 0.051=(0.596-0.051,\ 0.596+0.051)\\\\=(0.545,\ 0.647)$

Hence, the 95% (two-sided) confidence interval for the proportion of all dies that pass the probe.= (0.545, 0.647)