Lesson SG1

SG1 One sample t-test: AQA Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson SG1, One sample t-test: 20 multiple choice questions for the AQA Further Maths (7367), Unit 4: Optional application 2: statistics, written with Revision Ninja.

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The 20 questions

  1. What test statistic formula is used for a one-sample t-test of a population mean?

    • (x-bar - mu)/(s^2/n)
    • (x-bar - mu)/(sigma/sqrt(n))
    • (x-bar - mu)/s
    • (x-bar - mu)/(s/sqrt(n))

  2. For a one sample t-test with sample size n, how many degrees of freedom are used?

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

  3. In a one-sample t-test, what estimates the unknown population standard deviation sigma?

    • Population variance
    • Sample standard deviation
    • Sample mean
    • Standard error

  4. What underlying distribution assumption is required when conducting a small-sample one-sample t-test?

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

  5. What does the null hypothesis state in a one-sample t-test for a mean?

    • Mean equals mu0
    • Variance equals s^2
    • Mean exceeds mu0
    • Mean differs mu0

  6. For a two-tailed one sample t-test with 9 degrees of freedom at the 5% level, what is the critical value?

    • 2.093
    • 1.833
    • 2.262
    • 2.228

  7. For a one-tailed one sample t-test with 9 degrees of freedom at the 5% level, what is the critical value?

    • 1.833
    • 2.262
    • 2.821
    • 1.383

  8. A sample of size n = 10 has sample mean 52 and sample standard deviation 4. Test H0: mu = 50. What is the t statistic, to 3 decimal places?

    • 1.581
    • 0.500
    • 2.000
    • 1.265

  9. A sample of size n = 10 is used in a one sample t-test. What are the degrees of freedom?

    • 9
    • 8
    • 11
    • 10

  10. A t-test yields a statistic of 1.581 against a critical value of 2.262. What is the conclusion?

    • Reject H0
    • Retain H0
    • Invalid test
    • Accept H1

  11. A sample of size n = 16 has mean 20.5 and standard deviation 2. Test H0: mu = 20. What is the t statistic?

    • 4.0
    • 2.0
    • 1.0
    • 0.5

  12. A sample of size n = 25 has mean 103 and standard deviation 10. Test H0: mu = 100. What is the t statistic?

    • 5
    • 3
    • 1.5
    • 0.3

  13. For a two-tailed test at the 5% level with 24 degrees of freedom, what is the critical t value?

    • 2.492
    • 2.064
    • 1.318
    • 1.711

  14. A sample of 9 values has sum of squared deviations from the mean equal to 32. What is the sample standard deviation s?

    • 8/9
    • 2
    • sqrt(32/9)
    • 4

  15. In a one-tailed test with critical value 1.833, observed t = 1.9. What is the decision?

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

  16. For a two-tailed test at the 1% level with 9 degrees of freedom, what is the critical t value?

    • 2.821
    • 3.250
    • 3.690
    • 2.262

  17. A sample of 4 values is 4, 6, 8, 10. Test H0: mu = 6. What is the t statistic, to 3 decimal places?

    • 0.775
    • 2.582
    • 1.000
    • 0.387

  18. A two-tailed test has critical value 2.131. Observed t = -2.5. What is the decision?

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

  19. Which distribution is used for a mean test when the population variance is unknown?

    • t-distribution
    • Chi-squared distribution
    • Normal distribution
    • Poisson distribution

  20. Observed t = 2.8. Critical values: 5% is 2.179, 1% is 3.055. What is the conclusion?

    • Reject at 5%
    • Do not reject
    • Reject at 1%
    • Reject at both

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