
IB Math AI SL 4.11 – Hypothesis Testing & Significance
This lesson introduces students to the process of hypothesis testing, guiding them through the logic of statistical inference and decision-making under uncertainty. Students learn to formulate the null hypothesis (H₀) and alternative hypothesis (H₁), understand the concept of a significance level (α), and interpret p-values as probabilities of observing outcomes as extreme as the sample data under H₀.
The slide deck covers both one-tailed and two-tailed tests, emphasizing contextual conclusions and correct phrasing such as “fail to reject H₀” or “reject H₀.” Students explore three key applications: the chi-squared test for independence, used to determine whether two categorical variables are related; the chi-squared goodness-of-fit test, used to check whether data conforms to an expected distribution; and the t-test, used to compare means between two normally distributed populations. Each test includes step-by-step examples with data tables, calculator methods, and interpretations at common significance levels (1%, 5%).
By the end of the lesson, students can design and evaluate statistical tests, compute test statistics and degrees of freedom, and justify their conclusions with statistical reasoning. Fully aligned with IB Math AI SL Topic 4.11 – Hypothesis Testing and Significance, this resource develops foundational analytical skills essential for interpreting real-world data, assessing claims, and conducting valid inferential analysis.
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