Consider that your company just received a box of 500 widget

Consider that your company just received a box of 500 widgets from a new supplier. You would like to know about how many of the widgets are defective. What would be your strategy to create a confidence interval for the proportion of defective widgets in the box? Include sampling strategy, number in sample, and statistical analysis.

Solution

The good sampling method here is haphazard sampling since you can select the samples that are just defective... Purposive sampling might work too to determine the exact characteristics of samples, but pretty limited.

z test can be used here.

Let say n samples is tested and mean came is mu and standard deviation SD.

z = (mu / (SD/sqrt(n))

Confidence interval : (mu +_ z*SD/sqrt(n)) {Here z is as per the confidence interval that is asked for}