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3.7. Statistical Inference (INF)

This knowledge area covers the foundations and methods of statistical inference: point and interval estimation, hypothesis testing, likelihood theory, Bayesian inference, nonparametric methods, multiple testing, and large-sample theory. It is the core of classical and modern statistics.

Knowledge Area (KA)	Core Tier1	Core Tier2
3.7.1 Point Estimation	1	1
3.7.2 Interval Estimation and Confidence Intervals	1	1
3.7.3 Hypothesis Testing Foundations	1	1

3.7.1. INF/Point Estimation  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Methods for estimating unknown parameters from data. Covers desirable properties of estimators, method of moments, maximum likelihood estimation, and the Cramer-Rao lower bound.
Topics:
Core

• Desirable properties: unbiasedness, consistency, efficiency, and sufficiency
• Method of moments estimation: derivation and asymptotic properties
• Maximum likelihood estimation: derivation, properties, and invariance principle
• Cramer-Rao lower bound and the concept of Fisher information

Learning Outcomes:
Core:

1. Describe the key properties of estimators and explain the trade-offs between them [Familiarity]
2. Derive method of moments and MLE estimators for standard distributions [Usage]
3. Evaluate the efficiency of an estimator using the Cramer-Rao lower bound [Assessment]

3.7.2. INF/Interval Estimation and Confidence Intervals  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Construction and interpretation of confidence intervals. Covers pivotal quantity method, large-sample intervals, and the relationship between confidence intervals and hypothesis tests.
Topics:
Core

• Constructing confidence intervals using pivotal quantities and exact distributions
• Correct interpretation of confidence intervals: coverage probability and common misconceptions
• Large-sample confidence intervals based on asymptotic normality
• Duality between confidence intervals and hypothesis tests

Learning Outcomes:
Core:

1. Construct confidence intervals for means, proportions, and variances using exact and large-sample methods [Usage]
2. Interpret confidence intervals correctly and identify common misinterpretations [Usage]
3. Explain the duality between confidence intervals and hypothesis tests and use it to draw inferences [Assessment]

3.7.3. INF/Hypothesis Testing Foundations  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

The Neyman-Pearson framework for hypothesis testing: null and alternative hypotheses, Type I and II errors, power, p-values, and the most powerful tests.
Topics:
Core

• Neyman-Pearson framework: null/alternative hypotheses, rejection regions, Type I and II errors
• p-values: definition, correct interpretation, and common misuse; power and sample size
• Common parametric tests: z-test, t-test, F-test, chi-squared test
• Neyman-Pearson lemma and uniformly most powerful tests

Learning Outcomes:
Core:

1. Explain the logic of hypothesis testing, Type I and II errors, and the meaning of a p-value [Familiarity]
2. Apply standard parametric tests and interpret the results in context [Usage]
3. Derive the most powerful test for a simple hypothesis using the Neyman-Pearson lemma [Assessment]