Lesson SH1-SH2

SH1-SH2 Confidence intervals for a mean from large samples Quiz: AQA Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson SH1-SH2, Confidence intervals for a mean from large samples: 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 normal population with known variance sigma^2, which expression gives the symmetric 95% confidence interval for the population mean from a sample of n observations with mean xbar?

    • xbar ± 1.645 × sigma/sqrt(n)
    • xbar ± 1.96 × sigma^2/n
    • xbar ± 1.96 × sigma × sqrt(n)
    • xbar ± 1.96 × sigma/sqrt(n)

  2. What is the standard error of the sample mean for n independent observations from a population with standard deviation sigma?

    • sqrt(sigma/n)
    • sigma^2/sqrt(n)
    • sigma/n
    • sigma/sqrt(n)

  3. Which z value gives a symmetric 99% confidence interval for a normal mean, using the standard normal distribution?

    • 2.326
    • 1.645
    • 1.960
    • 2.576

  4. Which z value gives a symmetric 90% confidence interval for a normal mean?

    • 1.282
    • 2.576
    • 1.645
    • 1.960

  5. In repeated sampling, what proportion of 95% confidence intervals contain the population mean?

    • 99%
    • 5%
    • 90%
    • 95%

  6. A sample of n = 36 is taken from a normal population with known sigma = 6. The sample mean is 50. What is the 95% confidence interval for the population mean?

    • (48.04, 51.96)
    • (48.04, 52.96)
    • (49.00, 51.00)
    • (44.12, 55.88)

  7. A sample of n = 25 from a normal population with known sigma = 2 has mean 17.3. What is the symmetric 99% confidence interval for the population mean, to 2 decimal places?

    • (16.27, 18.33)
    • (15.97, 18.63)
    • (16.52, 18.08)
    • (17.30, 18.70)

  8. If the sample size n is quadrupled, how does the confidence interval width change?

    • It halves
    • It stays constant
    • It doubles
    • It quarters

  9. A normal population has known sigma = 4.5. What is the smallest sample size for a symmetric 95% confidence interval for the mean to have total width at most 2?

    • 39
    • 78
    • 156
    • 77

  10. A sample of n = 100 from a population with unknown variance has mean 24.6 and standard deviation 5.2. Using the large-sample method, what is the approximate symmetric 95% confidence interval for the mean?

    • (14.41, 34.79)
    • (23.26, 25.94)
    • (23.58, 25.62)
    • (24.08, 25.12)

  11. Why can the sample standard deviation s replace sigma for large samples?

    • s removes bias
    • s equals sigma
    • s estimates sigma
    • s reduces size

  12. A symmetric 95% confidence interval for a population mean is (12.1, 15.9). What is the sample mean used to construct it?

    • 14.0
    • 3.8
    • 15.9
    • 13.0

  13. A symmetric 95% confidence interval for a population mean is (12.1, 15.9). Assuming the z-based method, what is the standard error used?

    • Approximately 1.900
    • Approximately 0.950
    • Approximately 0.969
    • Approximately 3.724

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

    • It shifts right
    • It becomes wider
    • It becomes narrower
    • It remains unchanged

  15. A sample of n = 16 from a normal population with known sigma gives the 95% confidence interval (42.0, 48.0) for the mean. What is sigma, to 3 significant figures?

    • 3.06
    • 12.2
    • 1.53
    • 6.12

  16. A normal population has known sigma = 3. What is the smallest sample size needed for a symmetric 95% confidence interval for the mean to have margin of error at most 0.5?

    • 138
    • 277
    • 139
    • 35

  17. A symmetric 90% confidence interval is to be found for the mean of a normal population with known sigma = 10, using n = 25 observations with sample mean 60. What is the interval?

    • (56.08, 63.92)
    • (53.42, 66.58)
    • (58.00, 62.00)
    • (56.71, 63.29)

  18. Before sampling, what is the probability that a random 95% confidence interval contains the population mean?

    • 0.95
    • 0.05
    • 1.00
    • 0.50

  19. For a small sample with unknown variance, what effect does using z instead of t have?

    • Interval too narrow
    • Interval becomes asymmetric
    • Mean shifts right
    • Interval too wide

  20. A sample of n = 400 from a population with unknown variance has mean 50 and standard deviation 8. What is the approximate symmetric 95% confidence interval for the mean?

    • (48.43, 51.57)
    • (49.61, 50.39)
    • (42.16, 57.84)
    • (49.22, 50.78)

All AQA Further Maths quizzes