Learning objectives
By the end you can:
- State the hypothesis-testing framework precisely, null and alternative hypotheses, a test statistic, a significance level chosen in advance, a decision rule, and a p-value defined correctly (not as "the probability H0 is true"), and apply it uniformly across z, t, chi-square, and F tests.
- Define Type I error, Type II error, and power, compute power for a stated alternative, and solve for the sample size a test needs to hit a target power.
- Choose correctly between an independent-samples test and a paired (matched-samples) test for comparing two means, and show numerically why the wrong choice changes the conclusion.
- Run a chi-square test for a population variance and for independence/goodness-of-fit in a contingency table, and an F-test for the equality of two variances, reading each from its own distribution and degrees of freedom.
- Test a correlation coefficient for statistical significance and separate that from its economic size.
- Derive and interpret simple linear regression by hand, the least-squares slope and intercept, the standard error of the slope, the t-test and confidence interval on a coefficient, and state the assumptions (Gauss–Markov) that make that inference valid.
- Extend to multiple regression: read a partial slope correctly ("holding the other regressors constant"), compute R² and adjusted R², and run the overall F-test for joint significance.
- Diagnose the four classic regression diseases (heteroskedasticity, serial correlation, multicollinearity, and misspecification) name the test for each (Breusch–Pagan, Durbin–Watson, VIF, RESET), state what each disease does and does not break, and apply the fix.
- (Productivity objective: R10 duality.) Know precisely where this concept layer hands off to code (DA1.05) and use an AI copilot to accelerate that handoff, while stating the assumptions and verifying every diagnostic yourself, because the model cannot be trusted to know when its own regression is sick.
- Build every worked computation with at least one India (₹) and one US ($) example, on synthetic-but-fully-specified data, so the mechanics transfer across both markets you operate in.
The duality, stated once (R10). Objectives 1–8 and 10 are the understanding objective the mastery gate rewards, you earn the pass by computing and interpreting these statistics yourself, closed-book. Objective 9 is the productivity payoff you keep: knowing exactly which forthcoming tool builds this at scale, and refusing to trust its output until you have checked it against what you know by hand.
Prerequisites & connections
Builds on. QM1.01 (Probability, Distributions, Sampling & Estimation), this module assumes you already hold the normal, t, chi-square, and F distributions, the Central Limit Theorem, sampling distributions, and point/confidence-interval estimation as working tools; a hypothesis test is a confidence interval's more decisive sibling, built from exactly that machinery. EX2.03 (Financial & Statistical Functions) already taught you to produce a regression in one Excel cell (SLOPE, INTERCEPT, LINEST, CORREL, RSQ) and already warned you that R² is not causation, that small samples and spurious trends fool a fit, and that extrapolation is a guess dressed as arithmetic. This module does not re-teach any of that. It builds the layer underneath the cell: where the standard errors in LINEST's second row actually come from, what a coefficient's t-test is asking, what the F-statistic in row four is testing, and: beyond EX2.03's four warnings, the four additional, regression-specific failure modes (heteroskedasticity, serial correlation, multicollinearity, misspecification) that a clean R² can hide entirely. M2.07 gave you a live preview of why this machinery matters: the Beneish M-Score is a fitted linear combination of eight ratios with published coefficients, and Altman's Z came from multiple discriminant analysis on 66 real companies. Neither module derived why those coefficients carry the weights they do, why a sample of 66 firms is thin evidence, or how you would test whether any one of those eight coefficients is statistically distinguishable from zero, this module hands you exactly that lens, aimable at any fitted model you meet from here on, including your own.