Which significance test perform with few samples, known standard deviation and experimental errors? And how?

#1
Dear guys,
a friend of mine asked me to help him in performing a significance test with his experimental data. Unfortunately I am not sure how to proceed since the problem is, in my opinion, presents some particularities. I am going to describe it below.

He measured a quantity x under particular experimental conditions, and he wants to test if his result agrees with the theoretical value of x, which is given by μ with standard error σ, taken from a textbook.
He made N=3 independent observations of x, which are x1, x2 and x3., and each observation is characterized by an experimental error εi, with i = 1, 2 or 3.
He wants to carry out a significance test to verify whether his results are in line with the theoretical value (null hypothesis) or not (alternative hypothesis), with a predetermined confidence level.

Which test is better to perform? I checked many examples on the net and in some texts, but I didn't find anything similar.
I think that the particularities in this exercise are the following:

1) N is low (<< 30), which leads me to perform a t-Student test. But, as far as I know, t test is used when standard deviation of the population is not known, which is not the case because we know the value of σ. Should we use z test even if N is low?

2) How to account for experimental errors εi of each sample in the chosen significance test?

Thank you