Hypothesis Testing for Tolerance Limits



Hey everyone!

I need some help with this problem. I have been given sizes of a certain part being manufactured. There are 6 size observations in each sample and there are 40 samples like these. I have to conduct a hypothesis test to verify if the machine settings are correct depending on if the part sizes lie within a tolerance limit, say between the sizes a and b.

Can someone help me out? i don't know which hypothesis test is valid here?