Ok. I have never came across a situation like this before so I am not quite sure if I could use T-Distribution to construct a confidence interval. I have to basically come up with a percent accuracy of the microscope to make accurate measurements. In short, I have to answer this question which my supervisor asked me, "Give me an interval which tells me that the actual length of a particular object is plus or minus the length that I got form a repeated measurements"

For example- If I make a repeated measurement of a cube for Type I gage study and observe a particular value (sample mean) what is the plus or minus percent value that the actual value of the cube will be?

Now I know that I could construct a 95% or 99% confidence interval and get a value that I could add and subtract to the sample mean and say that I am 95 or 99% sure that the populatation mena value is between this interval but the only situation where I have applied this way is when you have a population and you take a random sample and you hypothesize population mean from the sample.

But my deliemma is I am only using one part of which I am taking multiple measurements and as we know even measuring the same object multiple times does not give us the same value everytime. So in this situation can I still use T-distribution or is there any other methods to answer this question. Any help is appreciated and Thanks in advance.