Business Context

FinSight, a SaaS company, is reviewing quarterly marketing spend. The finance team wants a simple but statistically grounded explanation of budget variance and whether the observed overspend is meaningfully outside normal month-to-month fluctuation.

Problem Statement

You are given monthly budgeted and actual marketing spend for one quarter, plus historical monthly variance behavior from the prior year. Calculate the budget variance, express it in both absolute and percentage terms, and assess whether the quarter's average monthly variance appears unusually high relative to historical variation.

Given Data

Historical monthly budget variance from the previous 12 months had:

Requirements

1. Calculate monthly variance in dollars and variance percentage for each month.
2. Calculate total quarterly budget, total quarterly actuals, and total quarterly variance.
3. Compute the average monthly variance for the quarter.
4. Test whether the quarter's average monthly variance is significantly different from the historical mean using a one-sample z-test.
5. Interpret whether the overspend is likely normal fluctuation or a signal that budgeting assumptions may be off.

Assumptions

• Treat monthly variances as independent observations.
• Use the historical standard deviation of 5,000 as the population standard deviation for the test.
• Use a two-sided test at $\alpha = 0.05$.