# What are the degrees of freedom for the chisquared distribution for comparing values within a likelihood function?

Let's say I have a likelihood function for a vector X.

I get this as dnorm(X, mean(X), sd(X)

Obviously the MLE will be the mean here.

But let's say I want to compare some other value, like 4, to the MLE. I do dnorm(4, mean(X), sd(X)

Then -2*log(prod(dnorm(X, mean(X), sd(X))/prod(dnorm(4, mean(X), sd(X))) to get the log likelihood ratio.