Answer the statistical inference test below

STS3771 Statistical Inference Test 2 15/5/2020 1. Explain what is meant by the most powerful test at level between two simple hypotheses? /5/ 2. The strength Y of a product has the Weibull distribution with pdf; 1 ( ) , > 0, > 0 () = { 0, If is unknown and is known. The strength of a random sample of n products are, 1 , 2 , ... , . a) Find the form of the most powerful test of the null hypothesis = 0.5 against the alternative hypothesis = 1.0. /15/ b) Show that has an exponential distribution. /5/ c) Use 2 tables to find the critical region of the most powerful test at the 10% level when n=20. [Assume the result that if 1 , 2 , ... , are independent, each with an exponential 2 distribution, mean , then 2 has the 2 distribution.] /5/