Lesson SH3-SH4

SH3-SH4 Making inferences and small-sample intervals Quiz: AQA Further Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson SH3-SH4, Making inferences and small-sample intervals: 20 multiple choice questions for the AQA Further Maths (7367), Unit 4: Optional application 2: statistics, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. Which distribution is used for small-sample confidence intervals when variance is unknown?

    • Binomial distribution
    • Chi-squared distribution
    • t-distribution
    • Normal distribution

  2. Which expression gives the symmetric confidence interval for the mean of a normal population with unknown variance, from a small sample of size n with mean xbar and standard deviation s?

    • xbar ± t(n-1) × s × sqrt(n)
    • xbar ± t(n-1) × s^2/n
    • xbar ± t(n-1) × s/sqrt(n)
    • xbar ± z × s/sqrt(n)

  3. For a 95% symmetric confidence interval based on a sample of size 10, which t value should be used?

    • 2.093
    • 1.960
    • 2.228
    • 2.262

  4. A sample of n = 10 from a normal population has mean 20 and standard deviation 3. What is the 95% confidence interval for the population mean, to 2 decimal places?

    • (17.85, 22.15)
    • (18.14, 21.86)
    • (19.05, 20.95)
    • (16.20, 23.80)

  5. A 95% confidence interval for a mean is (17.85, 22.15). Is 18 a plausible mean at the 5% significance level?

    • No, 18 is outside
    • Yes, 18 is outside
    • Yes, 18 is inside
    • No, 18 is inside

  6. If two 95% confidence intervals for population means overlap, what does this prove about the means?

    • Nothing definitive
    • Means are equal
    • Difference is significant
    • Means are different

  7. A sample of n = 5 from a normal population with unknown variance has standard deviation s = 2. Using t = 2.776, what is the margin of error for a 95% confidence interval, to 2 decimal places?

    • 2.48
    • 1.75
    • 2.78
    • 1.96

  8. A sample has n = 5 and s = 2. Given t_4(0.995) = 4.604, what is the 99% margin of error?

    • 4.12
    • 2.06
    • 9.21
    • 4.18

  9. Compared to the standard normal distribution, how are the tails of the t-distribution described?

    • Lighter tails
    • Identical tails
    • Heavier tails
    • No tails

  10. What distribution does the t-distribution approach as degrees of freedom tend to infinity?

    • Chi-squared
    • Standard normal
    • Poisson
    • Uniform

  11. Two samples have s = 3, but n = 10 and n = 30. Which 95% confidence interval is wider?

    • Cannot be determined
    • The n = 10 interval
    • The n = 30 interval
    • Both are equal

  12. A sample of n = 20 from a normal population with unknown variance has mean 45 and standard deviation 6. What is the margin of error for a symmetric 95% confidence interval for the mean, to 2 decimal places?

    • 2.57
    • 3.20
    • 2.63
    • 2.81

  13. A 95% confidence interval based on n = 15 is (33.2, 40.8). What is the sample mean?

    • 37.0
    • 40.8
    • 7.6
    • 33.2

  14. A 95% confidence interval for a mean is (-0.4, 2.2). Should H0: mu = 0 be rejected at the 5% level?

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

  15. A symmetric 99% confidence interval for the mean of a normal population with known variance is (48.2, 53.8), from the same sample. What is the corresponding 95% confidence interval?

    • (47.15, 54.85)
    • (48.87, 53.13)
    • (49.20, 52.80)
    • (48.20, 53.80)

  16. A sample of n = 8 from a normal population with unknown variance has standard deviation s = 2.5. Using t = 2.365 with 7 degrees of freedom, what is the margin of error for a 95% interval for the mean, to 2 decimal places?

    • 2.21
    • 1.73
    • 2.37
    • 2.09

  17. What key assumption behind a t-interval fails when a small sample comes from a strongly skewed population?

    • Independence
    • Normality
    • Equal variance
    • Linearity

  18. A 95% symmetric confidence interval for a mean is computed as xbar ± 2.262 × s/sqrt(10), with s = 3. If xbar = 20, what is the upper limit, to 2 decimal places?

    • 21.86
    • 22.26
    • 26.79
    • 22.15

  19. A 95% confidence interval for a mean uses n = 10 observations (width 4.29). If the sample size increases to n = 40 with the same s = 3 and the same mean 20, the 95% t-interval has t = 2.023 with 39 degrees of freedom. What is its approximate width?

    • About 4.29
    • About 1.00
    • About 2.14
    • About 1.92

  20. How does increasing sample size affect the width of a confidence interval for a fixed confidence level?

    • Increases width
    • Decreases width
    • Doubles width
    • No change

All AQA Further Maths quizzes