Statistics Foundation · Lesson 4.3
Hypothesis testing framework.
Hypothesis testing is a structured way to judge whether observed data are surprising under a baseline assumption. This lesson develops null and alternative hypotheses, test statistics, null distributions, p-values, rejection regions and careful interpretation.
Lesson route
Build the testing framework step by step.
Confidence intervals asked which parameter values are plausible. Hypothesis testing starts with a specific parameter value and asks whether the observed data are unusually far from it.
0–15 min
Why hypothesis testing is needed
Understand hypothesis testing as a formal way to judge whether observed data are surprising under a baseline assumption.
15–35 min
Null and alternative hypotheses
Learn how H₀ represents the baseline claim and H₁ represents the direction or type of evidence being investigated.
35–60 min
Test statistics
Study how an estimate is standardised by its standard error to measure distance from the null value.
60–85 min
Null distributions
Understand the probability distribution of the test statistic if the null hypothesis were true.
85–110 min
P-values and rejection regions
Connect extremeness, tail areas, p-values and significance-level decision rules.
110–140 min
Statistical decisions
Learn how to reject or not reject H₀ while avoiding overclaiming, causation mistakes and practical-importance errors.
Mastery checklist
Students should understand tests as evidence against a null model.
State null and alternative hypotheses correctly.
Distinguish one-sided and two-sided tests.
Compute a standardised test statistic.
Explain the null distribution.
Interpret a p-value correctly.
Use a significance-level decision rule.
Explain reject versus fail to reject.
Separate statistical significance from practical importance.