## Context You work on a brokerage/investing app. The team is considering launching **fractional share trading** (users can buy/sell fractions of a stock/ETF instead of whole shares). ## Task 1. **Explain the expected benefits** of fractional shares for the business and for users. 2. Propose an **experimentation plan** to evaluate the launch: - What is the **primary success metric**? - What **diagnostic metrics** help explain movement? - What **guardrail metrics** ensure you don’t harm users or the business? - Define the **unit of randomization** (user/account/household/etc.) and the treatment/control experience. - Call out key risks: interference/network effects, novelty effects, seasonality, and any selection bias. 3. **Sample size / power** - Show how you would estimate the **required sample size** for the primary metric (state assumptions such as baseline rate/variance, MDE, \(\alpha\), and power). - If you need to **adjust the sample size mid-experiment**, explain a statistically valid approach. 4. **Constraint scenario** - If the required sample size is **too large** (you don’t have enough traffic or time), what do you do? Provide at least 3 practical options (design, metrics, variance reduction, ramp strategy, or alternative inference methods) and discuss tradeoffs. ## Output Provide a structured written plan, including metric definitions, assumptions used in power/MDE calculations, and a final recommendation on whether/how to launch.