Business Context

FinSight, a mid-market finance analytics company, wants to quantify whether monthly operating cash flow systematically differs from monthly accounting profit for its SaaS clients. This matters because management teams often treat profit as if it were cash available to spend.

Problem Statement

You are given 12 months of paired observations for one client: monthly net profit and monthly operating cash flow, both in thousands of dollars. Define the monthly difference as:

$D = \text{Cash Flow} - \text{Profit}$

Test whether the average monthly difference is zero, and estimate the size of the difference.

Given Data

Use a two-sided paired t-test at significance level $\alpha = 0.05$.

Requirements

1. State the null and alternative hypotheses.
2. Compute the sample mean and sample standard deviation of the paired differences.
3. Calculate the standard error and t-statistic.
4. Find 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 cash flow versus profit.

Assumptions

• Monthly observations are treated as paired measurements from the same business.
• Differences are approximately independent across months.
• The distribution of monthly differences is reasonably symmetric for a paired t-test with 12 observations.