Problem
Business Context
StreamCart, a subscription video platform, believed that a new annual pricing page would improve paid conversion. After a 3-week experiment, the product lead asked whether the initial hypothesis was supported by the data and, if not, how the team should pivot its research.
Problem Statement
You are given the A/B test results for the old pricing page (control) and the new pricing page (treatment). Determine whether the new page improved conversion, and explain how the research direction should change if the data does not support the original hypothesis.
Given Data
| Group | Sample Size | Paid Conversions | Conversion Rate |
|---|---|---|---|
| Control (old pricing page) | 18,400 | 2,282 | 12.40% |
| Treatment (new pricing page) | 17,900 | 2,094 | 11.70% |
Additional information:
| Parameter | Value |
|---|---|
| Significance level | 0.05 |
| Test type | Two-sided |
Requirements
- State the null and alternative hypotheses.
- Compute the sample conversion rates and the observed difference.
- Calculate the pooled proportion and standard error for a two-proportion z-test.
- Compute the z-statistic and p-value.
- Construct a 95% confidence interval for the treatment-minus-control conversion difference.
- Decide whether the initial hypothesis was supported.
- Based on the result, recommend how the team should pivot its research in business terms.
Assumptions
- Users were randomly assigned to control and treatment.
- Each user had one primary conversion opportunity.
- Independence holds across users.
- Sample sizes are large enough for normal approximation to the binomial.
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