I have a fairly simple question on statistics and hypothesis testing - I am currently running a few Monte Carlo simulations that randomly samples from a normal distribution to approximate the price of an underlying instrument that I'm investigating. I also know the true/expected value $\mu_0$, of the price of this instrument, and I want to conduct tests to see if the average value $\bar{x}$, produced from my simulations is reasonably close enough to the expected value on some confidence level. The number of simulations $n$ here is small ($<10)$, and I do not have any information on the population variance $\sigma$.
From my understanding, the appropriate test here would be to conduct a two-tailed $t$-test with the null hypothesis being that the sample mean (simulated) is reasonably close to the population mean (expected), and the alternative hypothesis is the opposite. Another potential method I'm looking into is to also see if the population mean falls within the confidence interval of the sample mean at different confidence levels. I am unsure if this is a good method in this situation, as I have tried to compute these tests and I found that the method of assessing confidence intervals was more stringent (accepted a higher number of alternative hypotheses) compared to the conventional two-tailed hypothesis test. Can anyone kindly advise me on this?
The confidence interval's method can be applied if the population is gaussian. Otherwise you have to assume a certain population 's distribution.
The alternative way is to do a non-parametric test, i.e. kolmpgorov-smirnov