(Solved): Let X1, ... , X10 be a random sample from N(0,0%), where o2 is a variance, but unknown. : (a) Find ...

Let X1, ... , X10 be a random sample from N(0,0%), where o2 is a variance, but unknown. : (a) Find the best critical region of size a = 0.05 for testing Ho : 0% = 1 vs. Hp : 01 = 2. (b) Does the family of the distribution has MLR property in Ll=1 X?? Justify your answer. (c) Find the UMP test of size a = 0.05 for testing Ho : 0% < 1 vs. H? : o? > 1. (d) Find the likelihood ratio test for the same hypotheses in (c). Discuss whether the two tests in (c) and (d) are equivalent or not.