5.06a Chi-squared tests on contingency tables Quiz: OCR Further Maths, Unit 2

The 20 questions

1. In a chi-squared test for independence on a contingency table, what is the null hypothesis?

   • Variables are independent
   • Variables are dependent
   • Data is normal
   • Means are equal

2. What is the formula for degrees of freedom in an r by c contingency table?

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

3. What is the minimum expected frequency required for each cell in a chi-squared test?

   • 1
   • 5
   • 30
   • 10

4. When must Yates' continuity correction be applied in a contingency table test?

   • In 2x2 tables
   • In 3x3 tables
   • When E is under 5
   • In all tables

5. How is the expected frequency of a cell in a contingency table calculated?

   • (Row x Col) / Total
   • (Row + Col) / Total
   • (Row - Col) / Total
   • Row x Col x Total

6. What is the standard formula for a cell's contribution to the chi-squared statistic?

   • (O - E) / E
   • (O - E)^2 / E
   • (O + E)^2 / E
   • (O - E)^2 / O

7. When comparing the calculated chi-squared statistic to the critical value, when is H0 rejected?

   • Calculated > critical
   • Calculated < critical
   • Calculated = critical
   • Calculated = 0

8. What action should be taken if an expected frequency in a table is less than 5?

   • Multiply frequencies
   • Discard cell
   • Ignore constraint
   • Combine categories

9. How many degrees of freedom does a 3 by 4 contingency table have?

   • 7
   • 5
   • 12
   • 6

10. In a contingency table, row total is 20, column total 25, grand total 50. What is E?

    • 10
    • 5
    • 12.5
    • 15

11. If an observed frequency is 15 and the expected frequency is 10, what is its chi-squared contribution?

    • 0.5
    • 2.5
    • 5
    • 1.25

12. What are the degrees of freedom for a standard 2 by 2 contingency table?

    • 4
    • 0
    • 1
    • 2

13. A row total is 40, column total is 30, and grand total is 120. Calculate expected frequency.

    • 20
    • 12
    • 10
    • 15

14. A contingency table cell has an expected frequency of 3.2. What step must be completed next?

    • Proceed with calculation
    • Divide by two
    • Combine adjacent categories
    • Apply Yates' correction

15. In a 2 by 2 table with O=12 and E=8, calculate the numerator before squaring in Yates' correction.

    • 3
    • 4
    • 4.5
    • 3.5

16. The calculated chi-squared is 7.82 and critical value is 5.991. What is the test outcome?

    • Accept H0
    • Increase sample size
    • Inconclusive
    • Reject H0

17. A 4 by 3 table has two rows combined due to small expected frequencies. What is the new v?

    • 3
    • 6
    • 2
    • 4

18. Using Yates' correction with O = 10 and E = 6, calculate the squared numerator value.

    • 12.5
    • 9.5
    • 12.25
    • 16

19. A 3 by 3 table has two rows merged to satisfy expected frequency requirements. What are the new dimensions?

    • 1 x 3
    • 2 x 2
    • 3 x 2
    • 2 x 3

20. How do degrees of freedom change when two columns in a 3 by 4 contingency table are combined?

    • Decreases by 3
    • Decreases by 1
    • Remains unchanged
    • Decreases by 2

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