Lesson 2.05f

2.05f Pearson's product-moment correlation hypothesis test: OCR Maths, Unit 15

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.05f, Pearson's product-moment correlation hypothesis test: 20 multiple choice questions for the OCR Maths (H240), Unit 15: Statistical Hypothesis Testing, written with Revision Ninja.

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The 20 questions

  1. What population parameter does Pearson's correlation coefficient estimate in a hypothesis test?

    • r
    • sigma
    • mu
    • rho

  2. What underlying distribution assumption is required for testing Pearson's correlation coefficient?

    • Uniform distribution
    • Bivariate normal
    • Binomial distribution
    • Standard normal

  3. What type of relationship does Pearson's product-moment correlation coefficient measure?

    • Linear correlation
    • Causal relationship
    • Non-linear correlation
    • Quadratic trend

  4. What is the standard null hypothesis H0 when testing for Pearson's correlation?

    • r = 0
    • r = 1
    • rho = 1
    • rho = 0

  5. What is the alternative hypothesis H1 for a test of positive correlation?

    • r > 0
    • rho > 0
    • rho != 0
    • rho < 0

  6. What is the alternative hypothesis H1 for a test of negative correlation?

    • r < 0
    • rho < 0
    • rho > 0
    • rho != 0

  7. A sample gives r = 0.65 with critical value 0.5139 at 5% significance. What is the decision?

    • Increase sample size
    • Accept H0
    • Change significance
    • Reject H0

  8. A correlation test yields a p-value of 0.03 at a 5% significance level. What is the decision?

    • Accept H0
    • Accept H1
    • Retain H1
    • Reject H0

  9. A correlation test gives a p-value of 0.08 at a 5% significance level. What is the conclusion?

    • Accept H1
    • Reject H0
    • Insufficient evidence
    • Prove H0 true

  10. What symbol represents the calculated Pearson correlation coefficient from sample data?

    • r
    • s
    • p
    • rho

  11. What range of numerical values can Pearson's correlation coefficient take?

    • -1 <= r <= 1
    • 0 <= r <= 1
    • -1 < r < 0
    • 0 < r < 1

  12. A sample correlation r = -0.62 is tested against a critical value of 0.5139 (two-tailed). What is the outcome?

    • Reject H0
    • Accept H0
    • Inconclusive result
    • Invalid calculation

  13. What does a sample correlation value of r = 0 indicate about the variables?

    • Strong non-linear link
    • Negative correlation
    • No linear correlation
    • Perfect correlation

  14. What happens to the critical value of r as sample size n increases?

    • It increases
    • It stays constant
    • It decreases
    • It becomes zero

  15. What does rejecting H0 in a Pearson correlation hypothesis test indicate?

    • Proof of causation
    • Zero correlation
    • Model is wrong
    • Evidence of correlation

  16. For a two-tailed correlation test at 5% significance, what probability lies in each tail?

    • 1%
    • 5%
    • 10%
    • 2.5%

  17. A sample has correlation r = 0.32 with critical value 0.4409. What is the correct decision?

    • Accept H1
    • Re-test at 1%
    • Reject H0
    • Do not reject H0

  18. Which relationship type can Pearson's correlation coefficient fail to detect despite a strong association?

    • Quadratic relationship
    • Negative linear
    • Positive linear
    • Perfect direct

  19. Why does a significant correlation between two variables not imply one causes the other?

    • Test is two-tailed
    • Data is biased
    • Sample is small
    • Correlation isn't causation

  20. What alternative hypothesis H1 is used for a two-tailed test of Pearson's correlation?

    • rho != 0
    • rho > 0
    • rho < 0
    • rho = 0

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