A simulation gave me the following density of data (grey histogram, blue kernel density estimation). Having an alternative input $I^*$ with the same distribution (green line), I would like to check whether $I^*$ belongs to my simulated data (hypothesis testing).
Is it correct that I have to look at the quantiles of my approximately normal distributed data in order to verify my hypothesis? Say for $\alpha = 0.05$ I calculate the $\alpha$-quantiles and if $I^*$ is located in this area, I reject the hypothesis?
I'm a stranger to hypothesis-testing and appreciate any help. Thank you!