Further Mathematics · AQA 7367 · Option S · Topic SE

Chi-squared tests for association

χ² tests for association using contingency tables.

  • 5 sub-topics
  • 4 in Year 12, 1 in Year 13
  • 60 practice questions
  • 5 animated lessons
Practice questions (60) Lessons Worksheets All AQA Further Mathematics topics

What the specification says

Every sub-topic AQA can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. SE1n × m contingency tablesY12
  2. SE2The χ² statistic and degrees of freedomY12
  3. SE3Convention that expected frequencies exceed 5Y12
  4. SE4Sources of association in contextY12
  5. SE5Yates' correctionY13

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Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 60 questions in this topic, free, no account needed.

Chi-squared tests for association

Easy

A small expected frequency · Year 12 · 1 mark

  1. In a chi-squared test, one expected frequency is less than 5. What should be done?
    (1)

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  1. The chi-squared distribution is a good approximation only when the expected frequencies are large enough.BB: Combine that class with a neighbouring one, and reduce the degrees of freedom to match

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Chi-squared tests for association

Medium

Degrees of freedom after combining · Year 12 · 1 mark

  1. A contingency table has 2 rows and 4 columns. Two of the columns are combined because of small expected frequencies. How many degrees of freedom does the test now have?
    (1)

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  1. The table now has 2 rows and 3 columns: (2−1)(3−1)(2 - 1)(3 - 1).CC: 2

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Chi-squared tests for association

Hard

Chi-squared test for association · Year 12 · 8 marks

Students were asked which club they prefer. SportMusicDramaYear 12494735Year 13403733\begin{array}{c|ccc} & \text{Sport} & \text{Music} & \text{Drama} \\ \hline \text{Year 12} & 49 & 47 & 35 \\ \text{Year 13} & 40 & 37 & 33 \end{array}
  1. (a)
    Test, at the 5% level, whether there is an association between year group and preferred club.
    (7)
  2. (b)
    Identify the cell that contributes most to the test statistic and comment on it in context.
    (1)
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Part (a)7 marks

  1. H0:no association, H1:associationH_0: \text{no association}, \ H_1: \text{association}
  2. All expected frequencies exceed 5, so no classes need combining.EE=row total×column totalgrand total: 48.38,45.66,36.96,40.62,38.34,31.04{}= \frac{\text{row total} \times \text{column total}}{\text{grand total}}: \ 48.38, 45.66, 36.96, 40.62, 38.34, 31.04
  3. X2=0.332X^2 = 0.332
  4. ν\nu=(2−1)(3−1){}= (2 - 1)(3 - 1)=2, cv{}= 2, \ \text{cv}=5.991{}= 5.991
  5. Do not reject H₀: there is insufficient evidence of an association.

Part (b)1 mark

  1. Year 13, Drama: observed 33 is more than the expected 31.0.

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