Business Context

StreamCart, an online marketplace, tested a new promotional email subject line to improve click-through rate (CTR). The marketing team wants to know whether the observed lift is real or just random variation.

Problem Statement

Use a hypothesis test to determine whether the new subject line produced a statistically significant change in CTR versus the current subject line.

Given Data

Use a two-sided test at significance level α = 0.05.

Requirements

1. State the null and alternative hypotheses.
2. Compute the sample proportions for control and treatment.
3. Calculate the pooled proportion and the standard error for a two-proportion z-test.
4. Compute the z-statistic and two-sided p-value.
5. Determine whether the result is statistically significant at the 5% level.
6. Calculate a 95% confidence interval for the difference in CTR.
7. Briefly explain what the result means for the email rollout decision.

Assumptions

• Recipients were randomly assigned to control and treatment.
• Each recipient appears only once in the experiment.
• Click outcomes are independent within and across groups.
• Sample sizes are large enough for the normal approximation to be reasonable.