Estimating Completed Registrations from a Super Bowl QR-Code Ad

Context

You are asked to estimate how many users complete registration from a single 30-second Super Bowl TV ad that displays a QR code, then quantify uncertainty, identify key drivers, and outline how to measure incrementality.

Given

• Unique TV viewers: 115,000,000
• QR visible: 30s (single 30s spot)
• Device-available rate: 82%
• Per-viewer scan propensity: p_scan ~ Beta(12, 780); mean = 12/(12+780) ≈ 1.515%
• 12% of scans are duplicates (same person)
• 4% of scans are bot/invalid
• Landing infrastructure drops 6% of requests at peak
• Among valid unique sessions reaching the landing page: 68% click "Start sign up"
• Baseline form completion (no incentive): 72%
• $15 coupon increases form completion odds by 25% (odds ratio OR = 1.25)
• SMS 2FA delivery success: 94%
• Among delivered, 3% fail verification (i.e., 97% pass)

Assume independence between steps unless otherwise stated.

Tasks

(a) Compute the expected number of completed signups.

(b) Provide a 95% credible interval using only the Beta uncertainty on scan propensity (treat all other rates as fixed).

(c) Perform a one-way sensitivity analysis to identify the top three drivers of variance in signups.

(d) Outline a measurement plan to estimate incremental signups (e.g., geo holdout or QR variant holdout) and give a sample-size formula to detect a 5% relative lift with 90% power at α = 0.05, using a baseline signup-per-impression rate derived from the assumptions.