χ² and t-tests
Hypothesis tests for IB Applications and Interpretation SL: chi-squared tests and the t-test, with worked IB exam questions.
A hypothesis test decides, using data from a sample, whether a claim about the population is credible or whether the data contradict it. In this topic you see three IB tests: the χ² test for independence (are two categorical variables related?), the χ² goodness-of-fit test (do the data follow a given distribution?) and the t-test (do the means of two groups differ?). The graphic display calculator (GDC) gives the -value and the test statistic; what earns the marks is setting up the hypotheses correctly, comparing with the significance level and concluding in the context of the problem.
Recommended order
Work through the sections in order: the χ² test for independence, the χ² goodness-of-fit test and the t-test. At the end you have the IB exam questions, grouped by type.
Normal distribution (topic 12).
Sections in this topic
χ² test for independence
How to carry out a χ² test for independence: hypotheses, expected frequencies, degrees of freedom, p-value and conclusion. IB Applications SL.
3 worked examples Section 2χ² goodness-of-fit test
Goodness-of-fit chi-squared test for IB Applications and Interpretation SL: hypotheses, expected frequencies, degrees of freedom, p-value and conclusion.
3 worked examples Section 3The two-sample t-test
Two-sample t-test for IB Mathematics: Applications and Interpretation SL: hypotheses, one or two tails, p-value on the GDC and conclusion.
3 worked examples End of topicIB exam questions for topic 13
IB exam questions on hypothesis testing: chi-squared test for independence and goodness of fit, and Student's t-test, with step-by-step solutions.
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