Lesson 2.05e

2.05e Hypothesis test for a population mean Quiz: OCR Maths, Unit 15

20 questions

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Lesson 2.05e, Hypothesis test for a population mean: 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. Which distribution models the sample mean of n observations from a Normal distribution?

    • Uniform distribution
    • Poisson distribution
    • Normal distribution
    • Binomial distribution

  2. What does Pearson's product-moment correlation coefficient measure between two variables?

    • Difference in means
    • Non-linear association
    • Causal relationship
    • Linear association

  3. What is the null hypothesis when testing for linear correlation in a population?

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

  4. Which mathematical symbol denotes the population correlation coefficient?

    • r
    • mu
    • rho
    • sigma

  5. What test statistic formula is used for a normal population mean?

    • (xbar - mu) / sigma
    • sqrt(n) * (xbar - mu) / s
    • (xbar - mu) / (sigma / sqrt(n))
    • sigma / (sqrt(n) * xbar)

  6. What is the full numerical range of Pearson's product-moment correlation coefficient?

    • -1 to 0
    • -1 to 1
    • 0 to 1
    • 0 to 100

  7. What decision is made if the p-value is less than the significance level?

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

  8. What type of test is used for H0: mu = 50 against H1: mu != 50?

    • One-tailed test
    • Non-parametric test
    • Paired test
    • Two-tailed test

  9. If X is Normal with variance 16 and sample size is 25, what is the standard error?

    • 0.8
    • 0.64
    • 3.2
    • 4.0

  10. A sample correlation r = 0.45 exceeds the critical value 0.3783. What is the conclusion?

    • Accept H1 directly
    • Reject H0
    • Accept H0
    • Inconclusive

  11. A calculated z-statistic of 1.50 is compared to a critical value of 1.6449. What is concluded?

    • Reject H0
    • Do not reject H0
    • Accept H1
    • Test invalid

  12. For critical threshold plus or minus 0.4438, a sample yields r = -0.51. What is the decision?

    • Reject H0
    • Inconclusive result
    • Do not reject H0
    • Accept H0

  13. When testing H0: rho = 0 against H1: rho < 0, which region leads to rejecting H0?

    • r = -c
    • r >= c
    • r <= -c
    • |r| >= c

  14. In a 5% two-tailed hypothesis test, what proportion of probability lies in each tail?

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

  15. A sample correlation r = 0.85 between study hours and test mark indicates what relationship?

    • Weak positive correlation
    • Perfect linear relation
    • Strong positive correlation
    • Strong negative correlation

  16. For sample size 16, standard deviation 4, sample mean 18, and population mean 20, find z.

    • -8
    • -2
    • -0.5
    • 2

  17. If a test yields a p-value of 0.032, at which significance level is H0 rejected?

    • 0.5% level
    • 0.1% level
    • 1% level
    • 5% level

  18. Why do standard PMCC critical value tables only test the null hypothesis rho = 0?

    • Distribution shape changes
    • r becomes bounded
    • Variance becomes zero
    • Sample size decreases

  19. If sample variance quadruples while sample size and mean difference stay constant, how does z change?

    • Halved
    • Doubled
    • Unchanged
    • Quartered

  20. Rejecting H0 for correlation between age and reaction time implies what?

    • Linear correlation exists
    • Variables are independent
    • The gradient is zero
    • Causation is proven

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