Question

2. Fasten-it-All produces wood screws. The screws must be manufactured to within certain tolerances or they are considered defective.  Using 99% confidence, a machine that may be producing more than 1.35% defective screws must be shut down. To test Machine 1, a QC inspector randomly samples 1500 screws.  The QC inspector’s random sample of 1500 screws contains 12 defective screws.   

1. Based on this sample, compute by hand (using the normal approximation to the binomial) and interpret a 99% confidence interval for Machine 1’s defect rate.  Confirm your result with Minitab. (NOTE: You must find the correct multiplier using Minitab.)

2. Based on the 99% confidence interval computed in a, what recommendation would you make regarding whether Machine 1 should be shut down?   

We are not 99% confident that Machine 1 will have a defective rate below 1.25%. Since there is a reasonable chance for the machine to have a defective rate of 1.25%, or more, we should shut down the machine.

3. Suppose the QC inspector decided, instead, that a 90% confidence interval could be used.  Compute by hand (using the normal approximation to the binomial) and interpret a 90% confidence interval for Machine 1’s defect rate?  Confirm your result with Minitab.   

4. Based on the 90% confidence interval computed in c, what recommendation would you make regarding whether Machine 1 should be shut down?  Briefly explain, how the same sample produced different recommendations in parts b and d.   

Answer 1