So, for fun, I am taking some of the data of calls from the call center I work at and trying to do some hypothesis testing on them, specifically the number of calls received in a week, and using a Poisson distribution to fit it. Due to the subject matter of my job, there are two types of weeks, let's call one of them on-weeks where I hypothesize there are more calls, and off-weeks where I hypothesize there are fewer.
I have a theory that the $\lambda$ from on-weeks (let's call it $\lambda_1$) is larger than that of the one from off-weeks (let's call it $\lambda_2$)
So the hypothesis I want to test is $H_0: \lambda_1 > \lambda_2, H_1: \lambda_1 \leq \lambda_2 $
I know how to test for one parameter (say $H_0: \lambda_1 > 1, H_1: \lambda_1 \leq 1 $) but not so sure how to go about doing 2 given a data set. Let's say I take two week's worth of data from each one $X_1 = 2$ and $X_2 = 3$ for the off-week and $Y_1 = 2$ and $Y_2=6$ for the on-week. Can someone help walk me though this simpler version such that I can apply it to a larger data set? Any help is appreciated, thank you.