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

*under particular experimental conditions, and he wants to test if his result agrees with the theoretical value of*

**x***, which is given by*

**x***with standard error*

**μ***, taken from a textbook.*

**σ**He made

*3 independent observations of*

**N**=*which are*

**x**,*and*

**x****1**,**x****2***, and each observation is characterized by an experimental error*

**x****3**.

**ε****i***,*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)

**is low (<< 30), which leads me to perform a**

*N**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

*Should we use*

**σ.***z*test even if

**is low?**

*N*2) How to account for experimental errors

*of each sample in the chosen significance test?*

**ε****i**Thank you