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. For a one sample t-test of the mean of a normal distribution with unknown variance, which statistic is used?

    • F = s1^2 / s2^2
    • z = (x-bar - mu) / (sigma / sqrt(n))
    • chi squared = sum of (O - E)^2 / E
    • t = (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 with unknown population variance, what is used in place of the population standard deviation?

    • The range of the sample
    • The sample standard deviation s
    • The population mean
    • The standard error of the mean from a known sigma

  4. Which assumption is needed for the one sample t-test for a mean?

    • The population is uniform on [0, 1]
    • The sample size is exactly 30
    • The population is Poisson distributed
    • The population is normally distributed

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

    • The population mean equals a specified value mu0
    • The sample standard deviation is zero
    • The population variance is zero
    • The sample mean is always larger than 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. For a sample with n = 10, mean 52, standard deviation 4, and H0: mu = 50, what is the conclusion at the 5% level with a two-tailed test?

    • Reject H0, since 1.581 is greater than 2.262
    • Do not reject H0, since 1.581 is less than 2.262
    • Reject H0, since 1.581 is greater than 1.833
    • Reject H1, since 1.581 is less than 2.262

  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. For a one-tailed test of H1: mu > mu0 at the 5% level with 9 degrees of freedom, a t statistic of 1.9 is observed. What is the conclusion?

    • The test cannot be carried out
    • Do not reject H0
    • Reject H0 in favour of H1
    • Reject H1 in favour of 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 of H0: mu = 50 against H1: mu not equal to 50 gives t = -2.5 with 15 degrees of freedom. The two-tailed 5% critical value is 2.131. What is the conclusion?

    • Reject H0 at 5% only if t is positive
    • Do not reject H0, since 2.5 is less than 3
    • Reject H0, since |t| = 2.5 exceeds 2.131
    • Do not reject H0, since t is negative

  19. Why is a t distribution used rather than a normal distribution in a one sample test when the population variance is unknown?

    • Because the variance is estimated from the sample, adding uncertainty
    • Because the population mean is unknown
    • Because the sample size is always small
    • Because the t distribution has a smaller variance than the normal

  20. A two-tailed one sample t-test with 12 degrees of freedom gives t = 2.8. The critical values are 2.179 for 5% and 3.055 for 1%. What is the conclusion?

    • Reject H0 at 5% but not at 1%
    • Reject H0 at 10% only
    • Do not reject H0 at 5%
    • Reject H0 at 1%

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