Probability as statistic:

Let X1,X2,--- ,Xn are i.i.d. samples from Uniform([0,6]), where 6 E (0.1] is an unknown parameter. You wish to test the null hypothesis H, :9 = 1 against the alternative H1 2 6 1. Find the likelihood ratio test of signicance level a: = 0.05. Compute the type I and type II errors, and compare that with those for the case n = 1 in (ii). Do we always get lower type I and type H errors by increasing n