Compute sample size and analyze A/B results

The baseline conversion rate is 5%. You need 90% power at $\alpha = 0.05$ (two-sided) to detect a 6% relative lift. Calculate the required sample size per variant for a Bernoulli outcome using a normal approximation, then adjust it for 10% bot traffic and a 7-day window under the assumption that days are independent. After the experiment runs: variant A has 50,000 users and 2,650 conversions; variant B has 49,500 users and 2,820 conversions, and there was one interim look at day 3. Compute the p-value and 95% confidence interval for the difference in proportions, apply a correction for the interim look (such as O’Brien–Fleming or Bonferroni), check for sample-ratio mismatch, and decide whether to ship while discussing the risks of Type S/M errors and baseline mis-specification.

Overview: This question assesses competence in experimental design and statistical inference for A/B testing, including two-proportion sample size calculation and sequential correction methods (e.g., O’Brien–Fleming or Bonferroni).