This question evaluates proficiency in product analytics, cohort and funnel analysis, retention and supply diagnostics, pricing and subscription economics, and experimentation design.
Context: The Los Angeles market is seeing a 10% month-over-month decline in completed rides on shared vehicles. You are asked to diagnose the drop and design actions, including a promotional subscription test.
(a) Decompose the decline into acquisition (new riders), activation, cohort retention, and supply constraints using cohort tables and time-of-day/geo cuts. List the exact plots/queries you would run and what each would prove or falsify.
(b) Enumerate plausible root causes (seasonality, price/ETA shifts, ops outages, competitor entry, etc.) and the minimal data to refute each.
(c) For a "$100/month unlimited after a 1-week free trial" offer, decide who should receive the trial (new users, churn-risk users, high-propensity payers) and why; define targeting rules.
(d) Provide the break-even formula for the trial: incremental LTV × conversion − CAC − variable costs − fraud loss ≥ 0; solve for the minimum conversion rate given inputs.
(e) Outline the A/B test design (unit, duration, sample size, stratification), guardrails (support load, refund rate, fraud), and success criteria for a 4-week run.
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