Binomial Distribution Significance Level
Let X have a Binomial distribution with the number of trials n=15 and with probability of "success" p. We wish to test Ho: p=0.30 vs. H1: p doesn't equal 0.30.
Reject Ho if the likelihood ratio <= 0.15. Find the significance level.
I know that if the likelihood ratio <= 0.15, then that means X<=1 or X>=9. The significance level is P(Reject Ho | Ho true) but I can't figure out how to find that. Any help would be appreciated.
Re: Binomial Distribution Significance Level
For your probability, you should recall that a conditional probability P(A | B) = P(A and B)/P(B) so if you can find P(A and B) you can get the conditional probability.
If you are in the rejection region, the probability is given by alpha (the alpha value) and this is when X <= 1 or X >=9.
Now the likelihood ratio is L(theta_est)/L(theta_max) so you will need to convert this back to a probability for the cutoff.
Recall that the likelihood is between 0 and 1 always and there is a connection between the relative likelihood and the probability.
Hint: What is the connection between relative log-likelihood and the p-values corresponding to this value?