Business Context

You’re a data scientist at CartJet, a high-volume e-commerce marketplace (~8M weekly active users) that is redesigning its checkout page to reduce friction and increase completed purchases. The product team ran a 10-day A/B test and is excited because the treatment shows a higher conversion rate.

In the launch meeting, a PM says: “The p-value is 0.03, so there’s a 97% chance the new checkout is better.” Another stakeholder says: “A p-value of 0.03 means only 3% of the observed lift is due to randomness.” You need to correct the interpretation and make a recommendation that’s statistically sound and business-relevant.

Problem Statement

Using the experiment results below, compute the p-value and then explain what the p-value does and does not mean in this hypothesis test. Finally, connect the statistical result to a rollout decision, including at least one caveat.

Given Data

Notes: Traffic split was 50/50 by user_id hash. A user is counted once (first exposure only).

Requirements

1. State the null and alternative hypotheses for whether the redesign changes conversion.
2. Compute the two-proportion z-test statistic using a pooled standard error under $H_0$.
3. Compute the (two-sided) p-value.
4. In 2–4 sentences, define the p-value in this context and explicitly address why the two stakeholder statements above are incorrect.
5. Make a rollout recommendation (ship / don’t ship / run longer / segment) and justify it with both statistical and practical considerations.

Assumptions and Constraints

• Random assignment and independence across users.
• Large-sample normal approximation is acceptable (check that $np$ and $n(1-p)$ are sufficiently large).
• You are not adjusting for multiple comparisons (assume this was the primary metric and primary test).