Business Context

StreamHub, a short-video app, launched a new creator referral feature and wants to know which statistical methods are most useful for evaluating product growth. Rather than answer conceptually, use the data below to quantify growth using several common methods.

Problem Statement

Assess whether the referral feature improved user growth and identify which statistical methods are most informative for this decision.

Given Data

Weekly new activated users were tracked for 8 weeks before launch and 8 weeks after launch.

Assume a simple linear trend model where launch effect is measured as a level shift after week 8.

Requirements

1. Compute the pre-launch and post-launch mean weekly activations.
2. Test whether the post-launch mean is significantly higher using a two-sample t-test at $\alpha = 0.05$.
3. Construct a 95% confidence interval for the difference in means.
4. Estimate the launch effect using a simple regression with an indicator for post-launch period.
5. Briefly explain which statistical methods are most useful here and why.

Assumptions

• Weekly observations are treated as approximately independent.
• Variance is stable across the two periods.
• No other major product or marketing changes occurred during these 16 weeks.
• The goal is directional product-growth assessment, not full causal attribution.