Application of T-Distribution

#1
Hello Guys,

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. :)
 

Dason

Ambassador to the humans
#2
I'd say a t-based confidence interval should be fine. We assume that the measurement errors are approximately normal so the measurements themselves will be normally distributed centered at the true value. You want to get a good idea about what that true value is so you make a confidence interval. I don't see any problems here.