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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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  • $\begingroup$ W=Y/B0 or W=Y/B? $\endgroup$
    – user158565
    Commented Nov 29, 2018 at 4:08
  • $\begingroup$ The question says Y/B0 $\endgroup$
    – Aishwarya Deore
    Commented Nov 29, 2018 at 11:57
  • $\begingroup$ But at the end of the first paragraph, it says W=Y/B. $\endgroup$
    – user158565
    Commented Nov 29, 2018 at 14:22
  • $\begingroup$ Yes. But that is the distribution of W. T is a different test statistic.T is not the same as W $\endgroup$
    – Aishwarya Deore
    Commented Nov 29, 2018 at 16:23

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