4B.7.1 One-sample t-test: Pearson Edexcel Further Maths, Unit 24

The 20 questions

1. What is the test statistic formula for a one-sample t-test?

   • (x̄ - μ) / s
   • (x̄ - μ) / (σ / √n)
   • (x̄ - μ) / (s / √n)
   • (x̄ - μ) / n

2. Which population assumption is required for a small-sample t-test?

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

3. Why does a t-distribution have heavier tails than a standard normal distribution?

   • Negative variance
   • Larger sample size
   • Estimation of σ
   • Loss of symmetry

4. Which formula gives the confidence interval for a mean with unknown population variance?

   • x̄ ± z × (σ / √n)
   • x̄ ± t × s
   • x̄ ± z × (s / n)
   • x̄ ± t × (s / √n)

5. What is the two-tailed 5% critical t value with 15 degrees of freedom?

   • 1.753
   • 2.947
   • 2.602
   • 2.131

6. For a one-sample t-test with H1: μ > μ0, where is the rejection region?

   • Both tails
   • Lower tail
   • Upper tail
   • Centre

7. What does the significance level of a hypothesis test represent?

   • Power of test
   • Type II error probability
   • Type I error probability
   • P-value magnitude

8. A sample of n = 16 has mean 52 and s = 6. Test H0: mu = 50 against H1: mu not equal to 50. What is the test statistic?

   • 1.50
   • 1.33
   • 0.33
   • 3.00

9. For t = 1.33 with 15 degrees of freedom and critical value 2.131, what is the conclusion?

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

10. A sample of n = 25 has mean 10.4 and s = 2. Test H0: mu = 10. What is the test statistic?

    • 2.0
    • 1.0
    • 0.2
    • 5.0

11. Using the sample in the previous setting (n = 25, mean 10.4, s = 2), what is the 95% confidence interval for the mean, to 2 decimal places? (t value with 24 df is 2.064.)

    • (8.40, 12.40)
    • (9.57, 11.23)
    • (9.97, 10.83)
    • (9.62, 11.18)

12. A sample of n = 9 has mean 23 and s = 4. Test H0: mu = 20 against H1: mu > 20 at the 5% level. What is the test statistic?

    • 0.75
    • 6.00
    • 2.25
    • 1.33

13. A sample of n = 10 has mean 5 and s = 2. What is the half-width of the 95% confidence interval for the mean, to 2 decimal places? (t value with 9 df is 2.262.)

    • 1.43
    • 0.63
    • 1.96
    • 2.26

14. Which assumption of a one-sample t-test is violated by a strongly skewed population?

    • Normality of population
    • Equal population variances
    • Independence of observations
    • Known population mean

15. A sample of n = 36 has mean 47 and s = 6. Test H0: mu = 50 against H1: mu not equal to 50. What is the test statistic?

    • -3.00
    • -6.00
    • 3.00
    • -0.50

16. For a test statistic t = 2.5 with 20 df, what is the two-tailed p-value, to 2 decimal places?

    • 0.02
    • 0.01
    • 0.10
    • 0.05

17. A sample of n = 17 has mean 50 and s = 8. What is the 95% confidence interval for the mean, to 2 decimal places? (t value with 16 df is 2.120.)

    • (46.00, 54.00)
    • (48.04, 51.96)
    • (45.89, 54.11)
    • (42.00, 58.00)

18. What is the test statistic t for n = 10, mean = 62, s = 8, testing H0: mu = 60?

    • 2.262
    • 0.250
    • 2.500
    • 0.791

19. How does decreasing the degrees of freedom affect the critical value of a t-test?

    • Increases critical value
    • Reduces variance
    • Decreases critical value
    • Has no effect

20. A two-tailed p-value is 0.04. Is a conclusion of 99% certainty mathematically correct?

    • Always true
    • Incorrect
    • Inconclusive
    • Correct

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