I am new here. Would like to ask a question on the sample size requirement for hypothesis testing following.
If I am drawing samples with 2 non correlated variables (say x,y) from a bivariate normal distribution(assumed) with unknown mean and variance.
I would need to determine the CEP or 50% of the population would fall into X < x and Y < y. How much sample size should I be taking?
What I have thought of:
I have tried to think of it as a binomial distribution problem as well (either sample is in or not in a certain radius r = sqrt(x^2 +y ^2) , and setting probability to be p =0.5 variance as p(1-p). Matching against the table for 50% confidence. I have calculated the sample size required to be ~480.
While examining some literature, I have found sample size for Gaussian distribution to be only around 20-30.
Am I making some wrong assumption? What is the more appropriate way to follow?