Lesson 5.07a-b

5.07a-b Basis of sign tests and Wilcoxon tests Quiz: OCR Further Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 5.07a-b, Basis of sign tests and Wilcoxon tests: 20 multiple choice questions for the OCR Further Maths (H245), Unit 2: Statistics (Y542), written with Revision Ninja.

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The 20 questions

  1. Which assumption is relaxed when using a non-parametric statistical test instead of a parametric test?

    • Continuous data
    • Normal distribution
    • Equal variances
    • Independent observations

  2. What parameter is tested in a standard single-sample sign test?

    • Mean
    • Median
    • Mode
    • Variance

  3. What type of data pairs are evaluated in a two-sample sign test?

    • Paired data
    • Unordered data
    • Independent data
    • Categorical data

  4. How are zero differences handled when calculating sample size for a sign test?

    • Counted as positive
    • Discarded completely
    • Split equally
    • Counted as negative

  5. Under the null hypothesis, which distribution models the test statistic of a sign test?

    • Normal distribution
    • Poisson distribution
    • Binomial distribution
    • Student t-distribution

  6. What is the probability parameter p used in the Binomial model for a sign test?

    • 0.5
    • 0.05
    • 0.1
    • 1.0

  7. What extra symmetry assumption does the Wilcoxon signed-rank test make about the population?

    • Symmetric distribution
    • Skewed distribution
    • Uniform distribution
    • Normal distribution

  8. How is the test statistic T calculated in a Wilcoxon signed-rank test?

    • Smaller rank sum
    • Total rank sum
    • Mean of ranks
    • Number of positives

  9. In a Wilcoxon signed-rank test, how are differences ranked before signs are attached?

    • By sample size
    • By original sign
    • In chronological order
    • By absolute magnitude

  10. If two differences tie for ranks 3 and 4 in a Wilcoxon test, what rank do they receive?

    • 3
    • 3.5 and 4.5
    • 4
    • 3.5

  11. What is the sum of all ranks for a sample size of n non-zero differences?

    • 2n + 1
    • n(n + 1) / 2
    • n(n - 1) / 2
    • n squared

  12. If the sum of positive ranks is 15 and n is 6, what is the sum of negative ranks?

    • 0
    • 21
    • 6
    • 15

  13. When should the Wilcoxon rank-sum test be used instead of the signed-rank test?

    • Categorical data
    • Two independent samples
    • Single sample
    • Paired samples

  14. Which other test name is equivalent to the Wilcoxon rank-sum test?

    • Mann-Whitney U test
    • Chi-squared test
    • Kruskal-Wallis test
    • Kolmogorov-Smirnov test

  15. In a Wilcoxon signed-rank test, when is the null hypothesis rejected?

    • Statistic > sample size
    • Statistic >= critical value
    • Statistic <= critical value
    • Statistic == 0

  16. When applying a normal approximation to a sign test, what is the variance of X ~ B(n, 0.5)?

    • 0.1n
    • 0.5n
    • 0.25n
    • n

  17. Which continuity correction is applied to a discrete test statistic x when finding P(X <= x)?

    • Add 0.5
    • Subtract 0.5
    • Add 1.0
    • Subtract 1.0

  18. Why is the Wilcoxon signed-rank test generally preferred over the sign test?

    • Ignores outliers
    • Uses magnitude information
    • Easier to calculate
    • Requires normal data

  19. What null hypothesis is tested in a two-sample Wilcoxon rank-sum test?

    • Equal population means
    • Identical population distributions
    • Zero correlation
    • Equal variances

  20. What is the expected value of the test statistic in a Wilcoxon signed-rank test for sample size n?

    • n(n + 1) / 2
    • n(n + 1) / 8
    • n(n + 1) / 4
    • n(2n + 1) / 4

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