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International Baccalaureate Mathematics

Statistics and Probability

These are the Transum resources related to the statement: "Formulation of null and alternative hypotheses, H0 and H1. Significance levels. p-values. Expected and observed frequencies. The Χ2 test for independence: contingency tables, degrees of freedom, critical value. The Χ2 goodness of fit test. The τ-test. Use of the p-value to compare the means of two populations. Using one-tailed and two-tailed tests".

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Furthermore

The IB AI Syllabus provides the following guidance and clarification:

Hypotheses

Students should express H0 and H1 as an equation or inequality, or in words as appropriate.

Chi-squared Test

Hand calculations of the expected values or the 𝜒2 statistic may enhance understanding.

If using 𝜒2 tests in the IA, students should be aware of the limitations of the test for expected frequencies of 5 or less.

t-Test

In examinations calculations will be made using technology.

At Standard Level, samples will be unpaired, and population variance will always be unknown.

Students will be asked to interpret the results of a test.

Students should know that the underlying distribution of the variables must be normal for the t-test to be applied. In examinations, students should assume that variance of the two groups is equal and therefore the pooled two-sample t-test should be used.

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