4B.5.5 Large sample confidence intervals Quiz: Pearson Edexcel Further Maths, Unit 22

The 20 questions

1. What parameter replaces population standard deviation sigma in a large-sample confidence interval when sigma is unknown?

   • Sample variance
   • Standard error
   • Sample standard deviation
   • Population mean

2. According to the Central Limit Theorem, what distribution does the sample mean approach for large samples?

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

3. What is the formula for a large-sample 95% confidence interval for a mean with unknown sigma?

   • x-bar +/- 1.96s/n
   • x-bar +/- 1.96s/sqrt(n)
   • x-bar +/- 2.576s/sqrt(n)
   • x-bar +/- 1.645s/sqrt(n)

4. What is the large-sample 95% confidence interval for mu_x - mu_y with unknown variances?

   • (x-bar - y-bar) +/- 1.96 (s_x^2 - s_y^2)/(n_x + n_y)
   • (x-bar - y-bar) +/- 1.96 sqrt(s_x^2/n_x + s_y^2/n_y)
   • (x-bar - y-bar) +/- 1.96 (s_x + s_y)/(n_x + n_y)
   • (x-bar - y-bar) +/- 1.96 sqrt((s_x^2 + s_y^2)/(n_x + n_y))

5. What minimum sample size is commonly considered large enough to apply the Central Limit Theorem?

   • 10
   • 100
   • 50
   • 30

6. Which distribution approximately models the standardized test statistic for a large sample with unknown sigma?

   • Exponential
   • Standard normal
   • Chi-squared
   • Uniform

7. Why can the z distribution replace the t distribution for very large sample sizes?

   • Variance becomes zero
   • z is exact
   • t approaches z
   • t becomes zero

8. A sample of n = 100 has mean 40 and s = 8. What is the 95% confidence interval for the population mean, to 2 decimal places?

   • (38.43, 41.57)
   • (36.08, 43.92)
   • (38.00, 42.00)
   • (39.22, 40.78)

9. A sample of n = 64 has mean 75 and s = 12. What is the 90% confidence interval for the mean, to 2 decimal places?

   • (70.00, 80.00)
   • (72.06, 77.94)
   • (73.50, 76.50)
   • (72.53, 77.47)

10. Sample A: n = 60, mean 9 with s = 5. Sample B: n = 80, mean 5 with s = 7. What is the 95% confidence interval for the difference of means, to 2 decimal places?

    • (1.00, 7.00)
    • (0.02, 7.98)
    • (3.00, 5.00)
    • (2.01, 5.99)

11. A sample of n = 100 has s = 8. What is the standard error of the sample mean?

    • 0.8
    • 8
    • 0.08
    • 1.6

12. A sample of n = 100 has s = 10. What is the width of the 95% confidence interval for the mean?

    • 19.6
    • 1.96
    • 0.98
    • 3.92

13. A sample of n = 49 has mean 20 and s = 3.5. What is the 99% confidence interval for the mean, to 2 decimal places?

    • (19.02, 20.98)
    • (16.50, 23.50)
    • (18.71, 21.29)
    • (18.00, 22.00)

14. What happens to critical values of the t distribution as degrees of freedom become very large?

    • Approach z values
    • Become zero
    • Tend to infinity
    • Remain constant

15. Two independent samples each have sample standard deviation 3 and 4, with n = 50 in both groups. What is the standard error of the difference of means, to 2 decimal places?

    • 1.00
    • 0.50
    • 0.71
    • 0.25

16. How does increasing sample size n affect the approximation of sigma by sample standard deviation s?

    • Variance doubles
    • No effect
    • Accuracy decreases
    • Accuracy improves

17. What is the smallest whole sample size n for a 95% confidence interval with half-width at most 0.5, when the sample standard deviation is about 6?

    • 24
    • 553
    • 144
    • 554

18. A sample of size n = 36 is taken from a skewed population. Is a z interval appropriate?

    • Only with sigma
    • No, sample small
    • Yes, by CLT
    • No, population skewed

19. Two independent samples each have n = 100 and s = 10 for both groups. What is the half-width of a 95% confidence interval for the difference of means, to 2 decimal places?

    • 1.41
    • 1.96
    • 2.77
    • 3.92

20. For large samples the difference of means is -2.5 with a standard error of 1. What is the two-tailed p-value, to 3 decimal places?

    • 0.006
    • 0.012
    • 0.994
    • 0.025

Related quizzes

• Concepts of standard error and confidence intervals Quiz · 4B.5.1-4B.5.2 · 20 questions
• Confidence limits for a mean and for a difference of means Quiz · 4B.5.3-4B.5.4 · 20 questions
• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
• Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions