5.05c-d Normal-based hypothesis tests and confidence intervals Quiz: OCR Further Maths, Unit 2

The 20 questions

1. Which distribution is used to test a normal population mean when the population variance is known?

   • Normal distribution
   • Student's t-distribution
   • Chi-squared distribution
   • Binomial distribution

2. Which distribution is used for a small sample mean test when population variance is unknown?

   • Standard Normal distribution
   • Student's t-distribution
   • Chi-squared distribution
   • F-distribution

3. What are the degrees of freedom for a single sample t-test with sample size 15?

   • 16
   • 13
   • 15
   • 14

4. What is the standard error of the mean for sample size 25 with population standard deviation 10?

   • 0.4
   • 2.5
   • 5
   • 2

5. What is the margin of error for a normal confidence interval with critical value z?

   • z divided by SE
   • SE divided by z
   • z plus SE
   • z times SE

6. What is the critical z-value for a symmetric 95% confidence interval?

   • 2.576
   • 1.960
   • 1.645
   • 1.282

7. What is the critical z-value for a symmetric 90% confidence interval?

   • 1.960
   • 1.645
   • 2.576
   • 1.282

8. What are the degrees of freedom for a paired t-test with 12 paired observations?

   • 11
   • 24
   • 12
   • 22

9. What assumption about variances is required to pool sample variances in a two-sample t-test?

   • Known population variances
   • Equal sample sizes
   • Equal population variances
   • Zero population variances

10. What are the degrees of freedom for a two-sample t-test with sample sizes 10 and 12?

    • 20
    • 21
    • 19
    • 22

11. Calculate the test statistic z when sample mean is 105, target mean is 100, and SE is 2.5.

    • 2.0
    • 0.5
    • 2.5
    • 1.0

12. What happens to the width of a confidence interval as sample size increases?

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

13. How does increasing the confidence level from 95% to 99% affect the interval width?

    • It remains unchanged
    • It becomes narrower
    • It becomes zero
    • It becomes wider

14. What is a Type I error in hypothesis testing?

    • Rejecting true null
    • Accepting false null
    • Rejecting false null
    • Accepting true null

15. What is a Type II error in hypothesis testing?

    • Rejecting true null
    • Rejecting false null
    • Accepting false null
    • Accepting true null

16. By what factor must sample size increase to halve the confidence interval width?

    • 16
    • 4
    • 2
    • 8

17. What conclusion is drawn if a test yields p-value 0.03 at 5% significance level?

    • Increase sample size
    • Accept H0
    • Test is invalid
    • Reject H0

18. How is unbiased sample variance s^2 calculated from sum of squared deviations SS?

    • SS / (n + 1)
    • SS / n
    • SS / sqrt(n)
    • SS / (n - 1)

19. Which theorem justifies using normal distribution for large samples from non-normal populations?

    • Binomial Theorem
    • Central Limit Theorem
    • Chebyshev's Theorem
    • Bayes' Theorem

20. What is the 95% confidence interval when sample mean is 50 and error margin is 3?

    • (44, 56)
    • (47, 50)
    • (48.5, 51.5)
    • (47, 53)

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