On my last exam, this was one of the question I got wrong. However this was the only question I didn't manage to figure out even after the exam. Can anyone help me? With part c) especially?
In order to test the null hypothesis that X has a uniform distribution on the interval $(0,1)$ against the alternative that X has a triangular distribution $[f(x) = 2x$ for $0 < x < 1]$ a random sample of size n is chosen. You want to find the most powerful test at significance level $\alpha = 0.10$
a) If $n = 1$, for what values of X do you reject the null hypothesis?
b) What is the power of the test in a)?
c) If n = 10, for what observations do you reject the null hypothesis?