Business Context

StreamBox, a video streaming app, noticed that users who receive more push notifications tend to have higher weekly watch time. A product manager asks whether sending more notifications causes higher engagement, or whether the relationship is only correlational.

Problem Statement

Use the observational data below to quantify the correlation between notifications and watch time, then explain why correlation alone does not establish causation. Finally, compare the observational result with a small randomized experiment.

Given Data

Observational user-level summary

Randomized experiment summary

Significance level: $\alpha = 0.05$

Requirements

1. Test whether the observational correlation is statistically different from 0.
2. Compute and interpret the 95% confidence interval for the observational regression slope.
3. Test whether the randomized experiment shows a significant causal effect on watch time.
4. Explain, in product terms, why the observational result may reflect correlation without causation.
5. Give one plausible confounder and one better identification strategy.

Assumptions

• Observational users are independent.
• Pearson correlation and linear regression assumptions are reasonable for this summary analysis.
• The experiment used random assignment and equal exposure windows.