Business Context

FinSight, a SaaS finance platform, is training analysts to distinguish accounting profit from cash flow when evaluating business health. A small sample of monthly company records is used to test whether average monthly profit differs materially from average monthly operating cash flow.

Problem Statement

A candidate claims that profit and cash flow are effectively the same in practice. Use the sample data below to test whether the mean monthly profit is different from the mean monthly operating cash flow for the same companies.

Given Data

The table shows monthly values in $ thousands for 10 companies. Because both metrics are observed for the same company and month, this is a paired-sample problem.

Assume the differences are approximately normally distributed. Test at a 5% significance level.

Requirements

1. State the null and alternative hypotheses.
2. Compute the sample mean difference and sample standard deviation of the differences.
3. Calculate the paired t-statistic.
4. Compute the two-sided p-value.
5. Construct a 95% confidence interval for the mean difference.
6. Explain, in business terms, what the result says about the difference between profit and cash flow.

Assumptions

• Each company contributes one independent monthly observation pair.
• The paired differences are approximately normal.
• Profit and operating cash flow are measured consistently across companies.