Need to identify correct confidence interval A manufacturer of precision gaskets makes gaskets in two grades A and B. In A, the precision gaskets thickness is far more critical than in B. The production run for A is very small, whereas the production run for B is very large.
What should be the right confidence intervals for testing the thickness of A & B ? What should be the appropriate sample size?
My understanding is that a higher confidence interval makes more sense if the precision of attribute is important. Can somebody help me here please?

I see this is a coursework question so this answer may not be very useful but here we go...
I wonder whether the confidence interval is the right statistic to decide whether the manufacturing process is good enough. The problem is that increasing sample size will reduce the CI and eventually you will virtually always reject the null hypothesis.
Regarding the width of the CI, if you want to ensure the process is good enough and you want to be conservative, perhaps you want to choose a narrow CI, like 80%. A narrow CI means that you consider a smaller range of (true) means as compatible with the observed data so a narrow CI gives you more stringent quality control.

Perhaps an alternative approach could be to assume that thickness measures come from a known distribution, e.g. Gaussian, with unknown parameters values. Then from your sample of i.i.d. observations you can estimate the parameters of the probability density function and get the probability that a gasket is within an accepted interval of thickness.
For example, your sample has mean = 11 and sd = 1 and you tolerate thinckness between 8 and 12. Then you have 0.1% chance of producing a gasket too thin and 16% chance of producing a gasket too thick (R code below). (Questions I'm not sure about just now: How large has the sample size to be to ensure a good enough estimate of mean and sd? How do you add margins of error around the % chance above?)
(too_low <- integrate(dnorm, -Inf, 8, mean= 11, sd= 1))
(too_high <- integrate(dnorm, 12, Inf, mean= 11, sd= 1))

