Estimate CTR lift with binomial tests and errors

In an A/B test, the control group records 10,000,000 impressions at a 1.20% CTR, while the treatment group records 10,000,000 impressions at a 1.23% CTR.

(a) Calculate the absolute lift and the relative lift, the pooled standard error, the z statistic, and the two-sided p value. Also give a 95% confidence interval for the relative lift.

(b) Suppose you checked results every day for 14 days without any alpha spending. Estimate roughly how much the Type I error rate inflates, and outline a corrected sequential design — either using alpha spending or a Bayesian approach that places a prior on the lift.

(c) If you are additionally monitoring 8 guardrail metrics, describe how you would keep familywise error or false discovery rate under control.

Overview: This question tests statistical inference for proportions, sequential monitoring, and control of multiple-comparison error — it probes familiarity with comparing CTRs via the binomial model, pooled standard errors, z-tests and confidence intervals, Type I error inflation caused by peeking, and FWER/FDR tradeoffs.