# Statistics and Probability

## 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

• the maximum number of rows or columns in a contingency table will be 4
• the degrees of freedom will always be greater than one. At SL the degrees of freedom for the goodness of fit test will always be n…1
• the 𝜒2 critical value will be given if appropriate
• students will be expected to use technology to find a p -value and the 𝜒2 statistic
• only questions on upper tail tests with commonly-used significance levels (1%, 5%, 10%) will be set
• students will be expected to either compare a p -value to the given significance level or compare the 𝜒2 statistic to a given critical value
• expected frequencies will be greater than 5.

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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