Lesson S5.3.1

S5.3.1 Hypothesis test for the mean of a Normal distribution Quiz: Pearson Edexcel Maths, Unit 15

20 questions

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Lesson S5.3.1, Hypothesis test for the mean of a Normal distribution: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 15: Statistical hypothesis testing, written with Revision Ninja.

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The 20 questions

  1. What distribution is assumed for the population when testing a normal mean with known variance?

    • Normal distribution
    • Student's t-distribution
    • Poisson distribution
    • Binomial distribution

  2. Which test statistic is used for the mean of a normal distribution with known variance?

    • T
    • Chi-squared
    • Pearson's r
    • Z

  3. What must be known about the population variance to use a Z-test for the mean?

    • It is zero
    • It is known
    • It is unknown
    • It is estimated

  4. What is the null hypothesis for a population mean mu testing against a specific value mu_0?

    • mu != mu_0
    • mu > mu_0
    • mu < mu_0
    • mu = mu_0

  5. If a test is two-tailed at a 5 percent significance level, what is the tail probability on each side?

    • 2.5 percent
    • 5 percent
    • 1 percent
    • 10 percent

  6. What is the standard error of the sample mean X-bar given sample size n and population variance sigma squared?

    • sigma / n
    • sigma / sqrt(n)
    • sqrt(sigma) / n
    • sigma squared / n

  7. Which type of alternative hypothesis indicates a one-tailed test looking for an increase?

    • mu = mu_0
    • mu != mu_0
    • mu < mu_0
    • mu > mu_0

  8. What is the critical region for a test defined by values less than the critical value called?

    • Lower tail
    • Upper tail
    • Central region
    • Two-tailed

  9. Calculate the test statistic Z if sample mean is 52, population mean 50, variance 16, and sample size 16.

    • 1
    • 4
    • 0.5
    • 2

  10. Find the Z critical value for a upper one-tailed test at the 5 percent significance level.

    • 1.9600
    • 1.2816
    • 2.5758
    • 1.6449

  11. Find the Z critical value for a two-tailed test at the 5 percent significance level.

    • 2.5758
    • 1.6449
    • 1.9600
    • 2.3263

  12. Determine the p-value area for a calculated Z of 2.0 in a one-tailed upper test.

    • 0.0228
    • 0.9772
    • 0.0500
    • 0.0456

  13. State the decision rule to reject H_0 if the test statistic falls inside what?

    • Confidence interval
    • Sample space
    • Acceptance region
    • Critical region

  14. What term describes the probability of rejecting a true null hypothesis?

    • Significance level
    • Power
    • P-value
    • Type II error

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

    • Rejecting false H_0
    • Accepting true H_0
    • Rejecting true H_0
    • Accepting false H_0

  16. If a sample mean gives Z = 2.33, do you reject H_0 at the 2 percent upper significance level (critical value 2.05)?

    • Reject H_0
    • Do not reject H_0
    • Accept H_0
    • Inconclusive

  17. What sample distribution property allows Z-tests to work for any sample size if the population is normal?

    • Uniform variance
    • Asymptotic bias
    • Central Limit Theorem
    • Exact normality

  18. How does increasing the sample size n affect the standard error of the sample mean?

    • Increases it
    • No effect
    • Decreases it
    • Doubles it

  19. What is the conclusion if the calculated p-value is less than the significance level alpha?

    • Retain H_0
    • Revise alpha
    • Accept H_0
    • Reject H_0

  20. What is the alternative hypothesis if testing for a decrease in the population mean?

    • mu > mu_0
    • mu < mu_0
    • mu = mu_0
    • mu != mu_0

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