A/B change in cancellation rate (before vs after)

Context: You are evaluating a small product tweak intended to reduce cancellations. Treat each trip request as a Bernoulli outcome (1 = canceled, 0 = not canceled) to start.

Observed data:

• Before: n1 = 50,000 requested trips, cancel rate p1 = 7.2%.
• After: n2 = 48,000 requested trips, cancel rate p2 = 6.6%.

Tasks:

1. Hypothesis test and CI
   • Choose an appropriate test for the change in cancellation rate. State H0 and HA.
   • Compute a 95% confidence interval for the absolute rate difference Δ = (p_after − p_before) and interpret it in practical terms.
2. Adjustment for confounding (city, hour-of-day)
   • Specify a logistic regression that adjusts for city and hour-of-day, and include one interaction you deem important.
   • Write the model formula, list key assumptions, and describe how you would check calibration and overdispersion.
3. Power and MDE
   • What per-arm sample size is required to detect an absolute change of 0.5 percentage points at α = 0.05 with 80% power (ignore clustering first)?
   • Then discuss how an intraclass correlation (ICC) of 0.02 at the driver level inflates the required N under a cluster-robust design. Show the design effect and the new N.
4. Nonparametric check (bootstrap)
   • Describe a bootstrap procedure to form a CI for the rate difference, stratified by city (stratified resampling).
   • Explain when this CI might be preferable to the z-approximation.