Suppose a dataset contains the selling price for one particular product, and this product could be sold from many resellers. This product could be sold in two ways, sold without rebate to the reseller and sold with rebate to the reseller. The numbers of transaction for product sold with and without rebate are different; one has about 140 samples and the other has about 130 samples.
My goal is to perform hypothesis testing on whether the average selling price for the product sold without and with rebate is the same。
My initial thought was to use two sample t-test, but since one product could be only sold with or without rebate, they are mutually exclusive events, so they do not qualify for the independence assumption for the two sample t-test. I then wanted to use the paired t-test, but it's not a traditionally "before-after" paired data, plus the fact that the numbers of samples for two groups are not equal.
The distribution of the selling price with rebate is highly skewed, e.g., there are many points around the average selling price and there are wide spread of events toward higher selling price. (Since the reseller is given a rebate on every product they sell, the reseller would of course to sell the product as high as possible to gain more rebate on each transaction)