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.

1Write down1 mark
2026
Write down the number of degrees of freedom.
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2find2 marks
A χ² test at the 10% level gives p = 0.12. State the conclusion.
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3find1 mark
A χ² test of independence concludes ''do not reject H₀''. State what this means.
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4State1 mark
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State one further assumption the test makes.
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5find2 marks
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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6find2 marks
A contingency table cell has row total 80, column total 60, grand total 240. Find its expected frequency.
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7find2 marks
A χ² test gives p = 0.018. State the conclusion at the 5% significance level.
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8find1 mark
Find the degrees of freedom for a 5×2 contingency table.
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9find2 marks
A χ² test gives χ²_calc = 2.9 and the critical value is 5.991. State the conclusion.
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10Write down1 mark
2026
Write down the null hypothesis.
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11find2 marks
A χ² test gives p = 0.21. State the conclusion at the 5% significance level.
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12find1 mark
Find the degrees of freedom for a 4×4 contingency table.
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13find1 mark
Find the degrees of freedom for a 2×3 contingency table.
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14find2 marks
A cell has row total 45, column total 100, grand total 150. Find its expected frequency.
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15find1 mark
State the degrees of freedom for a χ² goodness of fit test with 5 categories.
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16find1 mark
State the null hypothesis for a χ² goodness of fit test checking whether a die is fair.
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17find1 mark
A χ² test of independence concludes ''reject H₀''. State what this means about the two variables.
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18find2 marks
A χ² test gives χ²_calc = 4.2 and the critical value is 3.841. State the conclusion.
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19find1 mark
Find the degrees of freedom for a 2×2 contingency table.
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20find1 mark
State the null hypothesis for a χ² test of independence between two categorical variables A and B.
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