## A/B/n test: compute p-values and make a ship decision You ran an online A/B/n experiment with **1 control** and **2 treatment variants** (A/B/C). You are given a table of aggregated results with one row per group: **Table: `ab_results`** - `group` (STRING): one of `control`, `variant_1`, `variant_2` - `users` (INT): number of unique users exposed to the group - `conversions` (INT): number of users who converted (binary outcome) Assume: - Users are independently assigned and each user appears in exactly one group. - The metric is **conversion rate** = `conversions / users`. - You want to test whether each variant changes conversion rate vs control. - Use a two-sided test unless you justify a one-sided test. ### Tasks 1. Using Python, compute the **p-value** for: - `variant_1` vs `control` - `variant_2` vs `control` (State what statistical test you chose and why.) 2. Provide **95% confidence intervals** for the lift (difference in conversion rates) for each variant vs control. 3. Because there are **two** comparisons vs the same control, explain how you would handle **multiple testing** (e.g., Bonferroni, Holm, FDR), and how that affects your decision. 4. Interpret the results in plain language and recommend **ship / no-ship** (and under what conditions you’d run a follow-up experiment). Include any assumptions or caveats (e.g., sample size adequacy, novelty effects, missing data, metric definition issues).