Lesson 4B.7.2-4B.7.3

4B.7.2-4B.7.3 Paired and two-sample t-tests Quiz: Pearson Edexcel Further Maths, Unit 24

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 4B.7.2-4B.7.3, Paired and two-sample t-tests: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 24: t-tests, written with Revision Ninja.

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The 20 questions

  1. How many degrees of freedom are used in a paired t-test with n pairs?

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

  2. What is the pooled estimate of the common variance for two independent samples of sizes n1 and n2?

    • s_p^2 = (s1^2 + s2^2) / 2
    • s_p^2 = (n1 s1^2 + n2 s2^2) / (n1 + n2)
    • s_p^2 = ((n1 - 1) s1^2 + (n2 - 1) s2^2) / (n1 + n2)
    • s_p^2 = ((n1 - 1) s1^2 + (n2 - 1) s2^2) / (n1 + n2 - 2)

  3. What are the degrees of freedom for the pooled two-sample t-test?

    • n1 + n2
    • min(n1, n2) - 1
    • n1 + n2 - 1
    • n1 + n2 - 2

  4. Which assumption is required for a pooled two-sample t-test but not an unpooled t-test?

    • Independent observations
    • Equal sample sizes
    • Equal population variances
    • Normally distributed data

  5. When should a paired t-test be used instead of an independent two-sample t-test?

    • Matched pair data
    • Different population variances
    • Uncorrelated observations
    • Independent sample data

  6. Why is a paired t-test usually more powerful than an unpaired test for matched pairs?

    • Eliminates sample bias
    • Increases sample size
    • Reduces error variance
    • Increases critical value

  7. What is a 95% confidence interval for mu1 - mu2 when the variances are equal but unknown?

    • (x-bar - y-bar) +/- t(n1 + n2 - 2) sqrt(s1^2/n1 + s2^2/n2)
    • (x-bar - y-bar) +/- t(n1 + n2 - 2) s_p sqrt(n1 + n2)
    • (x-bar - y-bar) +/- z s_p sqrt(1/n1 + 1/n2)
    • (x-bar - y-bar) +/- t(n1 + n2 - 2) s_p sqrt(1/n1 + 1/n2)

  8. Five paired differences are 2, 4, 1, 3, 0. What is the t statistic for H0: mu_d = 0, to 2 decimal places?

    • 2.83
    • 0.71
    • 1.58
    • 2.00

  9. Two independent samples have n1 = 8, s1 = 3 and n2 = 10, s2 = 4. What is the pooled variance s_p^2, to 2 decimal places?

    • 12.50
    • 12.94
    • 14.00
    • 11.50

  10. Using s_p^2 = 12.94 with n1 = 8 and n2 = 10, what is the t statistic for a difference of means of 5, to 2 decimal places?

    • 5.00
    • 2.93
    • 1.71
    • 0.34

  11. For t = 2.93 with 16 df and two-tailed 5% critical value 2.120, what is the conclusion?

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

  12. Ten paired differences have mean 2 and standard deviation 4. What is the 95% confidence interval for the mean difference, to 2 decimal places? (t value with 9 df is 2.262.)

    • (-2.00, 6.00)
    • (1.14, 2.86)
    • (0.00, 4.00)
    • (-0.86, 4.86)

  13. Two independent samples have n1 = 10 with s1^2 = 4 and n2 = 20 with s2^2 = 9. What is the pooled variance s_p^2, to 2 decimal places?

    • 6.00
    • 8.25
    • 6.50
    • 7.39

  14. A 95% confidence interval for (after minus before) is (-2.8, -0.2). What does this indicate?

    • Significant increase
    • Inconclusive result
    • No significant change
    • Significant decrease

  15. Two independent samples each have n = 5, with mean difference 4, and s1 = s2 = 2. What is the 95% confidence interval for mu1 - mu2, to 2 decimal places? (t value with 8 df is 2.306.)

    • (1.08, 6.92)
    • (1.67, 6.33)
    • (2.00, 6.00)
    • (0.09, 7.91)

  16. What is the consequence of incorrectly using an unpaired test on positively correlated paired data?

    • Increased test power
    • Smaller standard error
    • Reduced test power
    • Invalid critical value

  17. Fifteen paired differences have mean 1.2 and standard deviation 2.0. What is the t statistic for H0: mu_d = 0, to 2 decimal places?

    • 0.62
    • 1.20
    • 2.32
    • 3.87

  18. Two independent samples have standard deviations 2 and 8. Is a pooled t-test appropriate?

    • Yes, samples independent
    • No, sizes small
    • Yes, sizes equal
    • No, variances differ

  19. Six paired differences are 3, 2, 4, 1, 5, 3. What is the t statistic for H0: mu_d = 0, to 2 decimal places?

    • 2.45
    • 3.00
    • 1.41
    • 5.20

  20. What is the primary advantage of pooling sample variances in a t-test?

    • Removed skewness
    • Better variance estimate
    • Larger sample size
    • Smaller mean difference

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