Analyze a geo rollout and interpret charts

On 2025-07-15 you roll out a fresh onboarding experience restricted to Texas and Florida. Seven days later, leadership spots a 3% drop in nationwide DAU on a line chart. Lay out an analysis and respond with precision:

1. Causal question: did the rollout shift DAU within the treated states? Name the estimand and write the difference-in-differences (DiD) formula out in full.

2. Given this summary (daily averages, pre = 2025-06-15..2025-07-14, post = 2025-07-15..2025-08-14): Texas pre=500k, post=515k; Florida pre=300k, post=303k; control pool (all other states) pre=2,000k, post=2,060k. Work out the DiD for each treated state separately and for the two combined (population-weighted). Explain what the sign and the size mean.

3. That same chart also shows a recurring weekend trough and an apparent break on 2025-07-20. Sketch a segmented regression over the time series that quantifies the immediate level shift and the slope shift for treated versus control. Give the regression equation and explain how you would cluster the standard errors.

4. Guardrail metrics: suggest a minimum of three (crash rate, p95 latency, payment decline rate, for instance). Specify decision thresholds and say which of them are one-sided and which are two-sided.

5. Power and duration: with combined average daily DAU of 815k in the treated group, a relative MDE of 0.5% on DAU, alpha=0.05 and power=0.8, estimate how many days are required under a parallel-trends DiD. List your assumptions and say whether CUPED or synthetic controls would shorten the required duration.

6. The chart turns noisy near 2025-07-27, following a marketing campaign in California. Describe how you would validate the parallel trends assumption and how you would choose a donor pool or weights to limit spillovers.

7. Give a short go/no-go call, along with the exact additional data you would request to de-risk that decision.

Overview: This question probes causal inference and product analytics competencies — in particular how causal estimands and difference-in-differences are specified, segmented (interrupted) time-series regression, power and duration computation, spillover and donor-pool diagnostics, and how guardrail metrics are selected.