Lesson SE1-SE3

SE1-SE3 Contingency tables and expected frequencies Quiz: AQA Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson SE1-SE3, Contingency tables and expected frequencies: 20 multiple choice questions for the AQA Further Maths (7367), Unit 4: Optional application 2: statistics, written with Revision Ninja.

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The 20 questions

  1. What is a contingency table used to show?

    • Frequencies of observations classified by two categorical variables
    • The probability density of a single variable
    • Continuous measurements against time
    • The exact mean of a population

  2. For a contingency table, which formula gives the expected frequency E in a cell?

    • Row total divided by column total
    • Row total plus column total divided by 2
    • (Row total x column total) / grand total
    • Grand total divided by the number of cells

  3. Which statistic is used in a chi squared test for association?

    • Sum of O divided by E
    • Sum of (O - E) squared times E
    • Sum of (O - E) squared divided by E
    • Sum of (O - E) divided by E

  4. For an r x c contingency table, what are the degrees of freedom in a chi squared test for association?

    • r - c
    • (r - 1)(c - 1)
    • r c - 1
    • r + c - 2

  5. What is the usual convention for expected frequencies in a chi squared test?

    • All observed frequencies should be less than 5
    • All expected frequencies should be exactly 5
    • Expected frequencies should always be integers
    • All expected frequencies should be greater than 5

  6. What is the null hypothesis in a chi squared test for association?

    • The two variables are independent
    • The two variables are strongly correlated
    • The observed frequencies equal the grand total
    • The expected frequencies are all zero

  7. If an expected frequency in a chi squared test is less than 5, what is the usual action?

    • Change the significance level to 10%
    • Combine categories to increase the expected frequencies
    • Ignore the cell and carry on
    • Increase the observed frequencies by 5

  8. A 2 x 2 contingency table has observed frequencies 20, 30 in row 1 and 30, 20 in row 2. What is the expected frequency in the top left cell?

    • 50
    • 20
    • 30
    • 25

  9. For the same 2 x 2 table with observed frequencies 20, 30, 30, 20, what is the chi squared statistic?

    • 0.81
    • 3.24
    • 8
    • 4

  10. What are the degrees of freedom for a 2 x 2 contingency table in a chi squared test?

    • 2
    • 4
    • 1
    • 3

  11. What are the degrees of freedom for a 3 x 4 contingency table in a chi squared test?

    • 6
    • 12
    • 7
    • 3

  12. For a chi squared test with 1 degree of freedom at the 5% significance level, what is the critical value?

    • 2.706
    • 5.991
    • 7.815
    • 3.841

  13. A 2 x 2 table has row totals 40 and 60, column totals 30 and 70 and grand total 100. What is the expected frequency in row 1, column 1?

    • 28
    • 70
    • 12
    • 18

  14. A 2 x 2 table has row totals 40 and 60, column totals 30 and 70 and grand total 100. What is the expected frequency in row 2, column 2?

    • 18
    • 30
    • 42
    • 28

  15. A cell in a chi squared test has observed frequency 20 and expected frequency 15. What is its contribution (O - E)^2 / E to the statistic, to 2 decimal places?

    • 0.83
    • 1.67
    • 3.33
    • 5

  16. A 4 x 2 contingency table is used in a chi squared test. How many degrees of freedom are there?

    • 4
    • 1
    • 8
    • 3

  17. A 2 x 2 table has observed frequencies 30, 10 in row 1 and 20, 40 in row 2. What is the chi squared statistic, to 2 decimal places?

    • 4.5
    • 16.67
    • 8.33
    • 20

  18. A 5 x 3 contingency table is used in a chi squared test for association. How many degrees of freedom are there?

    • 12
    • 15
    • 4
    • 8

  19. A 3 x 2 contingency table has row total 90, column total 30, and grand total 300. What is the expected frequency in that cell?

    • 9
    • 30
    • 27
    • 3

  20. In a 2 x 2 table, what is the Yates term (|O - E| - 0.5)^2 / E for a cell with O = 20 and E = 25?

    • 1
    • 0.81
    • 0.36
    • 0.5

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