Business Context

A Research Analyst at Google is auditing whether purchase events in Google Analytics 4 are a valid and reliable source for reporting conversion rate on a Google Store landing page. To check reliability, the analyst compares GA4 purchase counts against the backend order system over 12 independent days.

Problem Statement

Use the sample of daily differences between the two systems to test whether GA4 is systematically biased relative to the backend source of truth, and quantify the uncertainty around that bias.

Given Data

Let the daily difference be defined as:

$\text{difference} = \text{GA4 purchases} - \text{backend purchases}$

Observed daily differences over 12 days:

Additional information:

Requirements

1. State the null and alternative hypotheses for testing validity.
2. Use a one-sample t-test to determine whether the mean difference is significantly different from 0.
3. Compute the test statistic and the two-sided p-value.
4. Construct a 95% confidence interval for the true mean difference.
5. Conclude whether GA4 appears valid enough to use as a reporting source.

Assumptions

• Daily differences are independent across days.
• The distribution of daily differences is approximately normal, or the t-test is acceptable for this small sample.
• The backend order system is treated as the reference source.