Business Context
StreamCart changed its signup page to reduce friction and increase completed account registrations. Before analyzing significance, the product team wants the hypotheses defined correctly for the primary metric: signup conversion rate.
Problem Statement
You are given results from a randomized A/B test comparing the old signup page (control) with a simplified signup page (treatment). Define clear null and alternative hypotheses for the product change, then test whether the treatment improved conversion.
Given Data
| Group | Sample Size | Signups | Conversion Rate |
|---|
| Control (old page) | 18,500 | 2,405 | 13.00% |
| Treatment (new page) | 18,900 | 2,646 | 14.00% |
Additional test settings:
| Parameter | Value |
|---|
| Significance level | 0.05 |
| Test type | One-tailed |
| Success metric | Signup conversion rate |
Requirements
- State the null hypothesis and alternative hypothesis in words and notation.
- Explain why a one-tailed test is appropriate or not appropriate in this product setting.
- Calculate the pooled conversion rate under the null hypothesis.
- Compute the standard error and z-statistic for a two-proportion z-test.
- Calculate the p-value and make a decision at α=0.05.
- Briefly interpret the result for the product team.
Assumptions
- Users were randomly assigned to control and treatment.
- Each observation is independent and each user is counted once.
- The normal approximation is valid because both groups have large sample sizes and enough conversions/non-conversions.
- The business goal is specifically to detect an improvement, not just any difference.
