Could you please take a look if my answer makes sense- I don't have a solution to this practice question. Also, I am not quite sure how to read the data in part (c).
Let be a random sample from an exponential distribution with density function
where is an unknown parameter.
(a) Obtain the likelihood ratio test statistic for testing against .
(b) State the assymptotic distribution of twice the logarithm of the likelihood ratio test statistic under Ho.
(c) If , will you reject the null hypothesis Ho at a significance level of 5%?
the MLE for is (I checked against a few sources).
Therefore my likelihood ratio
(b) the assymptotic distribution
(coverges in distribution)
(c) calculate r from the given test results.
Now I am not sure what is "Y" - if that is then why the MLE realisation ( ) is so far away from ?
Ideally I would use (b) to test the hypothesis.
Does the part (c) data make sense to you?