5.06b-d Goodness of fit and fitting theoretical distributions Quiz: OCR Further Maths, Unit 2

The 20 questions

1. What is the standard null hypothesis in a Chi-squared goodness of fit test?

   • Variables are independent
   • Means are equal
   • Model fits poorly
   • Model fits well

2. What is the minimum recommended expected frequency for any cell in a Chi-squared test?

   • 10
   • 30
   • 1
   • 5

3. How does pooling two adjacent cells affect the degrees of freedom in a test?

   • Decreases by 2
   • Decreases by 1
   • Increases by 1
   • No change

4. What is the formula for the test statistic component of each cell?

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

5. What is the base number of constraints lost in every goodness of fit test?

   • 3
   • 0
   • 1
   • 2

6. A Poisson model with estimated mean is fitted to k cells. What are the degrees of freedom?

   • k - 3
   • k
   • k - 2
   • k - 1

7. A Normal model with estimated mean and variance uses k cells. What are the degrees of freedom?

   • k - 3
   • k - 1
   • k - 4
   • k - 2

8. Which tail of the Chi-squared distribution is used for goodness of fit test critical regions?

   • Two-tailed
   • Symmetric tails
   • Upper tail
   • Lower tail

9. An observed frequency is 15 and expected frequency is 10. What is its Chi-squared contribution?

   • 0.5
   • 1.25
   • 2.5
   • 5

10. Calculate the expected frequency for a cell with total sample size 200 and probability 0.15.

    • 13.3
    • 15
    • 300
    • 30

11. What is the main purpose of pooling cells in a Chi-squared test?

    • Eliminate bias
    • Increase sample size
    • Ensure E >= 5
    • Reduce total observed

12. A fair six-sided die is rolled N times. What are the degrees of freedom?

    • 1
    • 4
    • 6
    • 5

13. A Binomial distribution with estimated p uses 8 cells. Find the degrees of freedom.

    • 7
    • 6
    • 5
    • 8

14. What alternative hypothesis is used in a Chi-squared goodness of fit test?

    • Mean is different
    • Variance is higher
    • Model fits poorly
    • Model fits well

15. A Geometric distribution with estimated parameter p is fitted to k cells. What are the degrees of freedom?

    • k
    • k - 3
    • k - 1
    • k - 2

16. What happens to the test statistic when observed and expected frequencies match perfectly?

    • Equals 1
    • Equals 0
    • Equals k - 1
    • Equals infinity

17. Five cells have expected frequencies 12, 10, 8, 4, and 2. How many cells remain after pooling?

    • 2
    • 5
    • 4
    • 3

18. A Binomial distribution with known parameter p is fitted to 6 cells. What are the degrees of freedom?

    • 4
    • 5
    • 3
    • 6

19. Why does estimating a population parameter from sample data reduce degrees of freedom?

    • Adds a constraint
    • Increases variance
    • Distorts expectations
    • Reduces sample size

20. If a calculated Chi-squared statistic exceeds the critical value, what decision is made?

    • Reject null hypothesis
    • Reject alternative hypothesis
    • Accept null hypothesis
    • Inconclusive result

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