Business Context

MarketHub, an online marketplace, tested a new promotional email subject line to increase purchase conversion from an email campaign. The marketing lead wants to know whether the observed lift is real enough to influence rollout, and how the p-value should be interpreted in a business decision.

Problem Statement

You are given the results of a randomized A/B test comparing the current subject line (control) with a new subject line (treatment). Determine whether the conversion lift is statistically significant and explain what the p-value does and does not mean for the business.

Given Data

Use a two-proportion z-test with significance level α = 0.05.

Requirements

1. State the null and alternative hypotheses.
2. Compute the pooled conversion rate.
3. Compute the standard error under the null.
4. Calculate the z-statistic and two-sided p-value.
5. Decide whether to reject the null hypothesis at the 5% level.
6. Interpret the p-value in plain business language.
7. Explain whether statistical significance alone is enough to launch the new subject line.

Assumptions

• Users were randomly assigned to control and treatment.
• Each user received only one version of the email.
• Purchases are independent across users.
• The normal approximation is appropriate because both groups have sufficiently large sample sizes and enough conversions/non-conversions.