Business Context

BrightCart, an e-commerce retailer, reviews monthly paid-search spend against budget. Finance wants to know whether this quarter's overspend is just normal month-to-month variation or evidence that the budget assumptions were materially wrong.

Problem Statement

Compare actual monthly spend against the monthly budget and determine whether the average overspend is statistically significant.

Given Data

The paid-search budget was fixed at \$500,000 per month for the last 6 months.

Assume monthly variances are approximately independent and normally distributed.

Requirements

1. Define the null and alternative hypotheses for whether mean variance is zero.
2. Compute the sample mean variance and sample standard deviation.
3. Use a one-sample t-test to test whether average actual spend differs from budget at $\alpha = 0.05$.
4. Construct a 95% confidence interval for the mean monthly variance.
5. Explain the likely drivers of the difference in business terms: signal vs normal fluctuation.

Assumptions

• Budget is a fixed target, not an estimate with uncertainty.
• The 6 months are representative of the current operating process.
• No major one-off campaign shocks occurred outside normal paid-search operations.