I have the following problem: in year A, we observe that a company sold N_A of its product, in year B, we observe that the company sold N_B of its products. How do I do hypothesis testing that the company sold statistically different number of products in year A and B?
My thought is that
N_A ~ Poisson(lambda_A)
N_B ~ Poisson(lambda_B)
So my hypothesis test is
H_0: lambda_A = lambda_B
H_1: lambda_A != lambda_B
Then I can run a z-test where the test statistic
Z = |N_A - N_B|/sqrt(N_A + N_B)
follows a normal distribution with mean 0 and variance 1.
Is this the correct method? If so, why can the Z-test be applied in this case?