Hi,
For the question above, how do I find the likelihood statistic if I'm not told what the distribution, mean or variance is?
For part 1, should I be testing H0 against H1: p isn't 1/2?
Similarly in part 2, should I be testing H0 against H1: p isn't the same for each country?
Could anyone help guide me through answering this question? I've just started learning about the likelihood statistic and I'm not entirely sure about how to proceed.
Thanks a lot!
Right, you are looking for two simple hypotheses. In part 1, you're testing
$H_0: p=\frac{1}{2}$
$H_1: p\neq\frac{1}{2}$
In part 2, the same idea is true. As for the distribution, think about what makes sense. In this case, we have a 'Is male' and a 'Is not male" outcome. Can you think of a distribution we could use to model this? For example, a continuous distribution wouldn't really make any sort of sense, such as the exponential.
Once you've determined your distribution, you should correctly be able to formulate the likelihood ratio test statistic using it and the two simple hypotheses.