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