I would venture to guess that is a poisson rv and thus the variance is the same as the mean.

(By the way I never sleep)

If these are Poisson's then you have as n goes to infinity

but we can use the Law of Large Numbers and Slutsky's Theorem.

There we have

So If this is a Poisson we can use either as estimate of

or use the null hypothesis value as the estimate of the unknown variance.

I'm making this guess since n is greater than 30 so I would guess they want to use the CLT.

And if there isn't a sigma, we need to find a relationship between moo and sigma.

Night Poisson Ivy