Question:

Let X be a binomial random variable with n trials and probability of success, p. What is the generalized likelihood ratio for testing H0: p = .5 vs HA: p =/ .5?

Show that the test rejects for large values of |X - n/2|.

I know the likelihood ratio in this case to be the likelihood function @ p = .5 divided by the likelihood function @ p = mle of p but I cannot get anything that makes sense in terms of a test statistic.

Thanks in advance for any help you can provide.