Lesson 5.08a-d

5.08a-d Pearson's product-moment correlation and its hypothesis test: OCR Further Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 5.08a-d, Pearson's product-moment correlation and its hypothesis test: 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. What range of values can Pearson's product-moment correlation coefficient take?

    • 0 to 1
    • -0.5 to +0.5
    • -1 to +1
    • -∞ to +∞

  2. What type of relationship between two variables does PMCC measure?

    • Linear
    • Exponential
    • Quadratic
    • Non-linear

  3. In a hypothesis test for PMCC, what does the symbol ρ represent?

    • Sample correlation
    • Population correlation
    • Sample mean
    • Population variance

  4. What is the standard null hypothesis for testing if two variables are correlated?

    • ρ = 0
    • r = 0
    • ρ = 1
    • r = 1

  5. How are the degrees of freedom calculated for a PMCC test with n paired observations?

    • n
    • 2n - 1
    • n - 2
    • n - 1

  6. If sample correlation r equals 1, what does this indicate about the scatter plot?

    • Weak positive linear
    • No linear association
    • Perfect positive linear
    • Perfect negative linear

  7. Which transformation applied to a dataset changes the value of the PMCC?

    • Multiplying by two
    • Linear scaling
    • Adding a constant
    • Non-linear transformation

  8. If a sample gives r = -0.85, how is the linear correlation described?

    • Strong positive
    • Weak negative
    • Strong negative
    • Weak positive

  9. Which statistical distribution is used for the PMCC test statistic when testing ρ = 0?

    • Chi-squared distribution
    • Normal distribution
    • Student's t-distribution
    • F-distribution

  10. What formula calculates the t test statistic for testing H0: ρ = 0?

    • r√(n-2)/√(1-r²)
    • r√(n-1)/√(1-r²)
    • r√ n/√(1-r²)
    • r²√(n-2)/(1-r)

  11. What assumption about the bivariate data population is required for a PMCC hypothesis test?

    • Independence
    • Univariate normality
    • Bivariate normality
    • Uniformity

  12. A bivariate sample of size 10 gives r = 0.6. What are the degrees of freedom?

    • 8
    • 7
    • 9
    • 10

  13. For a two-tailed PMCC test, when do you reject the null hypothesis?

    • r > critical value
    • |r| > critical value
    • |r| < critical value
    • r < critical value

  14. What formula represents PMCC in terms of summary statistics S_xx, S_yy, and S_xy?

    • S_xy/√(S_xx + S_yy)
    • S_xy/√(S_xx S_yy)
    • S_xx/√(S_xy S_yy)
    • S_xy/(S_xx S_yy)

  15. If all x-values are multiplied by 3, what happens to the sample correlation coefficient r?

    • Remains unchanged
    • Changes sign
    • Decreases
    • Triples

  16. If a test statistic t exceeds the critical value, what decision is made?

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

  17. What does a PMCC value of 0 indicate between two continuous variables?

    • Zero gradient
    • No linear correlation
    • Perfect correlation
    • Negative correlation

  18. For a test claiming negative correlation, what is the correct alternative hypothesis H1?

    • ρ = 0
    • ρ ≠ 0
    • ρ > 0
    • ρ < 0

  19. As sample size n increases for a fixed positive r, what happens to the p-value?

    • Decreases
    • Remains constant
    • Becomes one
    • Increases

  20. Which table is directly used to find critical values of r without calculating t?

    • Binomial table
    • Poisson table
    • Normal distribution table
    • PMCC critical table

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