I have a sequence $X_1,X_2,...,X_n$ of n=20 independent random variables that follow a normal distribution such that
$X_n \sim N(\mu,\frac{\sigma^2}{n}$)
Getting one unique sample of $X_n$ for each value of n, can I use the likelihood ratio testo to do hypothesis testing. Is there a problem if every sample belongs to a different population? As far as I understand it should be ok but books define the LR test for just one single population.
Thank you