Suppose a Machines defect production rate is unknown The QC

Suppose a Machine\'s defect production rate is unknown. The QC inspector’s random sample of 1000 screws contains 6 defects.

a. Based on this sample, compute by hand (using the normal approximation to the binomial) and interpret a 95% confidence interval for Machine 1’s defect rate.

b. Based on the 95% confidence interval computed in a, what recommendation would you make regarding whether Machine 1 should be shut down?

Solution

p = 6 / 1000 = 0.006

q = 1 - 0.006 = 0.994

alpha = 1 - 0.95 = 0.05

alpha / 2 = 0.025

Z= 1.96 [ from tables]

I: 0.006 +/- 1.96 * srqt [ (0.994 * 0.006) / 1000 ]

0.006 +/- 0.004786

0.001214 < p < 0.010786

0.1214 % < p < 1.0786%

b)

the recomendation would be that take a sample more bigger to see if there is more defects, and see the proportion of defects