Let W = Y/B0 be a Random variable that has a gamma(2n,1) distribution. [Y has a gamma(2n,B) distribution and W = Y/B].

i) Suppose you want to test H0 : B ≤ B0 against H1 : B > B0 for some B0 > 0. How would you use the statistic T = Y/B0 to obtain a test with size 5% when B = B0? Find the critical value when n = 24 and report it to three decimal places. [Hint: The invgammap in Stata will be useful.]

ii) Argue that B = B0 is the least favorable case under H0.

iii) Instead of finding a critical value, how would you find the p-value if the outcome of T is t? Report the p-value to three decimal places if n = 24 and t = 39. 4.

I know how to do it if T follows a normal distribution. How do I do it in this question though? Any help will be appreciated - especially for part ii).


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