I'm trying to analyse the impact of a marketing campaign and I'm looking to identify the most appropriate statistical test. I have one group of customers who received the campaign (approx 100,000 people) and a random control (approx 50,000 customers) who received nothing. I want to measure whether there is any difference in the average spend from both groups in the period following the campaign launch.
The vast majority of customers in both groups will spend nothing after the campaign. Only approximately 2% of the customers in the groups will spend anything. So the average spend variable in both groups is not normally distributed - it will have a huge tail at 0, corresponding to the large number of people who will spend nothing.
As the population sizes are very large (100,000 and 50,000) can I just use a 2 sample z test as normal due to the central limit theorem? Or will the fact that the variable being tested is highly skewed mean that a 2 sample z test is invalid?