Lesson 2.05c

2.05c Sampling and significance Quiz: OCR Maths, Unit 15

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.05c, Sampling and significance: 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. If X ~ N(50, 16) and n = 4, what is the distribution of the sample mean?

    • N(50, 4)
    • N(25, 4)
    • N(50, 8)
    • N(50, 16)

  2. A sample is used in statistical hypothesis testing to make an inference about what?

    • The critical region
    • The population
    • The test statistic
    • The significance level

  3. If X ~ N(100, 25) and sample size n = 25, what is the variance of X_bar?

    • 1
    • 0.2
    • 25
    • 5

  4. What term describes the set of values of the test statistic that leads to rejecting H0?

    • Acceptance region
    • Rejection region
    • Sample space
    • Confidence interval

  5. If X ~ N(20, 9) and a sample of size n = 9 is taken, what is Var(X_bar)?

    • 9
    • 81
    • 3
    • 1

  6. When conducting a hypothesis test, what type of variable is the sample mean X_bar?

    • Population mean
    • Fixed constant
    • Random variable
    • Constant parameter

  7. If the significance level of a test is 5%, what is the maximum Type I error probability?

    • 0.95
    • 0.01
    • 0.50
    • 0.05

  8. If X ~ N(mu, 36) and n = 4, what is the standard deviation of X_bar?

    • 6
    • 3
    • 9
    • 1.5

  9. In a 1% significance level test, what is the probability of incorrectly rejecting H0?

    • At most 0.10
    • At most 0.01
    • At least 0.99
    • Exactly 0.05

  10. If X ~ N(40, 100) and n = 100, what is the standard error of the mean?

    • 10
    • 100
    • 0.1
    • 1

  11. What region on a test distribution corresponds to p-values smaller than the significance level?

    • Acceptance region
    • Critical region
    • Null region
    • Sample region

  12. If X ~ N(mu, sigma^2), what is the mean of the random variable X_bar?

    • mu
    • mu / n
    • n * mu
    • mu / sqrt(n)

  13. What value is compared against the significance level to decide whether to reject H0?

    • Standard error
    • Sample mean
    • p-value
    • Variance

  14. If X ~ N(10, 16) and sample size n = 16, what is the standard deviation of X_bar?

    • 1
    • 16
    • 0.25
    • 4

  15. Why do statisticians use a sample statistic instead of a population parameter?

    • Samples eliminate all bias
    • Population parameters are unknown
    • Calculations are prohibited
    • Populations are always small

  16. If a sample size n increases, what happens to the variance of the sample mean X_bar?

    • Becomes zero
    • Decreases
    • Increases
    • Stays constant

  17. What defines the critical value in a statistical hypothesis test?

    • Population variance limit
    • Boundary of rejection region
    • Observed test statistic
    • The sample mean value

  18. If X ~ N(0, 64) and n = 16, what is the distribution of X_bar?

    • N(0, 4)
    • N(0, 16)
    • N(0, 2)
    • N(0, 64)

  19. For a discrete test at a 5% significance level, the actual rejection probability is what?

    • At most 5%
    • At least 10%
    • Greater than 5%
    • Exactly 5%

  20. What does rejecting H0 at a specified significance level indicate?

    • Absolute certainty
    • Evidence against H0
    • Proof H0 is false
    • Proof H1 is true

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