4B.6.1 Hypothesis test for a population variance Quiz: Pearson Edexcel Further Maths, Unit 23

The 20 questions

1. Under H0: sigma^2 = sigma0^2, what is the test statistic for a sample of size n with sample variance s^2?

   • n s^2 / sigma0^2
   • (n - 1) s^2 / sigma0^2
   • (n - 1) sigma0^2 / s^2
   • (n - 1) s / sigma0

2. In any hypothesis test, what defines a Type I error?

   • Accepting true H0
   • Rejecting false H0
   • Rejecting true H0
   • Accepting false H0

3. What population distribution is assumed when conducting a chi-squared test for a population variance?

   • Poisson
   • Binomial
   • Uniform
   • Normal

4. What is the null hypothesis when testing whether a population variance equals a specified value sigma_0^2?

   • H0: mu = sigma_0^2
   • H0: sigma = x-bar
   • H0: s^2 = sigma_0^2
   • H0: sigma^2 = sigma_0^2

5. For an upper-tailed chi-squared test, when is H0 rejected?

   • Below critical value
   • Exceeds critical value
   • Is negative
   • Equals zero

6. Which option best describes the shape of a chi-squared distribution?

   • Negatively skewed
   • Positively skewed
   • Symmetrical
   • Bimodal

7. What probability lies above a 5% upper critical value?

   • 0.50
   • 0.025
   • 0.05
   • 0.95

8. A sample of n = 10 has s^2 = 8. Test H0: sigma^2 = 4. What is the test statistic?

   • 20
   • 18
   • 5
   • 4.5

9. Test statistic = 18, critical value = 16.919. What is the conclusion for H1: σ² > 4?

   • Test invalid
   • Accept H0
   • Do not reject H0
   • Reject H0

10. A sample of n = 16 has s = 3. Test H0: sigma = 2 against H1: sigma > 2. What is the test statistic?

    • 6.67
    • 22.50
    • 33.75
    • 36.00

11. Test statistic = 33.75, critical value = 25.00. What is the test conclusion?

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

12. A sample of n = 12 has s^2 = 5. Test H0: sigma^2 = 2 against H1: sigma^2 not equal to 2. What is the test statistic?

    • 2.27
    • 30.00
    • 13.75
    • 27.5

13. When H0 is true, what is the expected value of the statistic (n - 1)s^2/sigma^2?

    • sigma^2
    • n - 1
    • 1
    • n

14. A lower-tailed chi-squared test has statistic 3.2 and critical value 3.325. What is the conclusion?

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

15. A sample of n = 20 has s^2 = 10. Test H0: sigma^2 = 4 against H1: sigma^2 > 4. The 1% upper critical value for 19 df is 36.19. What is the test statistic?

    • 19.0
    • 7.6
    • 47.5
    • 50.0

16. What factor besides sample variance affects the significance of a chi-squared variance test?

    • Population mean
    • Sample size
    • Median
    • Expected value

17. For a two-tailed variance test, statistic = 14 and critical values = 1.690, 16.013. Conclusion?

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

18. A sample of n = 10 has s^2 = 4. What is the 95% confidence interval for sigma^2, to 2 decimal places? (Chi-squared critical values for 9 df are 2.700 and 19.023.)

    • (4.00, 16.00)
    • (0.44, 3.33)
    • (1.89, 13.33)
    • (2.70, 19.02)

19. For H1: sigma^2 > sigma0^2 with s^2/sigma0^2 fixed at 2, the statistic is (n - 1) x 2. By what factor does the statistic change when n increases from 10 to 40?

    • About 4.3, since 78/18 = 4.33
    • 2
    • 4
    • 16

20. Why are the lower and upper critical values for a chi-squared test not symmetric?

    • Variance is negative
    • Mean is zero
    • Sample size varies
    • Distribution is skewed

Related quizzes

• 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
• Goodness of fit tests for discrete distributions Quiz · 3B.6.1 · 20 questions
• Definition and derivation of probability generating functions Quiz · 3B.7.1 · 20 questions