Here is my problem. I have a large population of uncoated parts. The weight of the uncoated parts is normally distributed. I then apply a coating to the parts- the weight of the coating also being normally distributed. I take a sample of the parts before and after coating. I need to know the mean coating weight and the standard deviation of the coating and their confidence intervals.
I know how to calculate the mean coating weight, the standard deviation of the coating weight (square root of the difference in variances before and after coating), and confidence intervals for the mean. What I don't know is how to calculate the confidence interval for the standard deviation.
I know how to calculate the confidence interval for a sample standard deviation but not for a standard deviation calculated by taking the difference of two samples, each of which have their own inherent uncertainty.