Lesson 2.05d

2.05d Hypothesis test for a sample mean Quiz: OCR Maths, Unit 15

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.05d, Hypothesis test for a sample 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. If X ~ N(μ, σ²), what is the distribution of the sample mean X-bar for size n?

    • N(μ, σ²/n)
    • N(μ, nσ²)
    • N(μ/n, σ²/n)
    • N(μ, σ²)

  2. What is the standard deviation of the sample mean X-bar when X ~ N(μ, σ²)?

    • σ² / n
    • √σ / n
    • σ / n
    • σ / √n

  3. In a hypothesis test for a population mean, what does null hypothesis H0 state?

    • X-bar = μ0
    • μ > μ0
    • σ = σ0
    • μ = μ0

  4. What test statistic Z is used for a hypothesis test on a normal mean?

    • (X-bar - μ) / (σ²/n)
    • (X-bar - μ) / σ
    • (X-bar - μ) / n
    • (X-bar - μ) / (σ/√n)

  5. How does increasing sample size n affect the variance of the sample mean X-bar?

    • It increases
    • It decreases
    • It stays constant
    • It doubles

  6. What type of hypothesis test is used when the alternative hypothesis states μ ≠ μ0?

    • Binomial test
    • Two-tailed test
    • One-tailed test
    • Paired test

  7. If the p-value is less than the significance level, what is the correct decision?

    • Reject H0
    • Accept H1 as false
    • Do not reject H0
    • Reject H1

  8. What is the expectation E(X-bar) of the sample mean for X ~ N(μ, σ²)?

    • μ / n
    • nμ
    • μ / √n
    • μ

  9. If X ~ N(50, 16) and n = 4, what is the variance of X-bar?

    • 8
    • 16
    • 4
    • 2

  10. If X ~ N(100, 25) and n = 25, what is the standard error of X-bar?

    • 25
    • 0.2
    • 5
    • 1

  11. A sample of size 16 has mean 53. If X ~ N(50, 64), find test statistic Z.

    • 0.375
    • 1.5
    • 0.75
    • 3.0

  12. For a 5% one-tailed test with H1: μ > μ0, what is the critical Z value?

    • 1.645
    • 2.576
    • 2.326
    • 1.960

  13. For a 5% two-tailed test, what are the critical values of test statistic Z?

    • ±2.326
    • ±1.960
    • ±1.645
    • ±2.576

  14. If X ~ N(20, 9) and n = 9, what is the distribution of X-bar?

    • N(2.22, 1)
    • N(20, 3)
    • N(20, 1)
    • N(20, 9)

  15. If Z = -2.10 and critical value is -1.645 for H1: μ < 10, what decision is made?

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

  16. If sample mean X-bar = 105, H0: μ = 100, and σ/√n = 2.5, calculate Z.

    • 0.5
    • 5
    • 1.25
    • 2

  17. If sample size n is quadrupled, how does the standard deviation of X-bar change?

    • Unchanged
    • Quartered
    • Doubled
    • Halved

  18. If X-bar ~ N(50, 0.25) from sample size n = 100, what is the variance of X?

    • 250
    • 0.25
    • 25
    • 2.5

  19. For H0: μ = 0 against H1: μ > 0 at 1% significance level, what is critical region?

    • Z > 2.576
    • Z > 2.326
    • Z > 1.960
    • Z > 1.645

  20. A 2% two-tailed hypothesis test for μ uses which critical values for Z?

    • ±2.054
    • ±2.326
    • ±2.576
    • ±1.960

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