Unit 4: Statistics and Probability
Topic 4.11: Chi-Squared Test for Independence Questions
Practice 20 exam-style questions for IB Math AI SL Topic 4.11. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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State the null hypothesis for a χ² goodness of fit test checking whether a die is fair.
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Find the degrees of freedom for a 5×2 contingency table.
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State the degrees of freedom for a χ² goodness of fit test with 5 categories.
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A claim states a population is split 40%, 35%, 25% across three groups. For a sample of 200, find the expected frequencies.
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A χ² test gives p = 0.018. State the conclusion at the 5% significance level.
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A χ² goodness of fit test gives p = 0.30. State the conclusion at the 5% level.
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A cell has row total 45, column total 100, grand total 150. Find its expected frequency.
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A χ² test gives p = 0.21. State the conclusion at the 5% significance level.
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A χ² test at the 1% level gives p = 0.007. State the conclusion.
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State the formula relating degrees of freedom to the dimensions of a contingency table.
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A χ² goodness of fit test gives p = 0.002 at the 5% level. State the conclusion.
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State the alternative hypothesis for a χ² test of independence.
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A χ² test at the 10% level gives p = 0.12. State the conclusion.
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A spinner is claimed to land on each of 4 colours equally. It is spun 160 times. Find the expected frequency for each colour under H₀.
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Find the degrees of freedom for a 4×4 contingency table.
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State the null hypothesis for a χ² test of independence between two categorical variables A and B.
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Find the degrees of freedom for a 2×2 contingency table.
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Find the degrees of freedom for a 2×3 contingency table.
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Find the degrees of freedom for a 3×4 contingency table.
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A χ² test of independence concludes ''do not reject H₀''. State what this means.
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