PLEASE SOLVE USING PYTHON

Based on a time frame that is long enough, we know that our standard design (call it the STD) produces a CTR (click-through rate) of 10\%. We want to come up with a new design (call it NEW) hoping that it will improve our CTR and generate more revenue. The difference (MDE: minimum detectable effect) that we want to see is at least 2%. 1. Can you find the minimum sample size (per variant) needed to detect a 2% difference with a test power of 80% ? There are many different ways of finding it. statsmodels has a bunch of different modules to do what you want. Please explore what's out there and choose one to find the minimum sample size. Assume =0.05. 2. A healthy A/B test is possible when certain conditions are met. One method of finding out everything will work out as intended is to conduct an A/A test: Comparing the same variants. Van you build a simulation to see if the false positive rate (seeing an efect when there is none) coming out of the simulation is in agreement with the significance level of your choice? 3. Suppose, using the sample size you found in (1), you get the following table: Based on these CTR values obtained at the end of the expeirment, can you calculate the test power with a simulation