Lesson O1-O2

O1-O2 Hypothesis testing for a binomial proportion Quiz: AQA Maths, Unit 11

20 questions

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Lesson O1-O2, Hypothesis testing for a binomial proportion: 20 multiple choice questions for the AQA Maths (7357), Unit 11: Statistics, written with Revision Ninja.

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The 20 questions

  1. In hypothesis testing, what is the null hypothesis?

    • The statement being tested, usually a claim of no change or a stated value
    • A statement about the sample rather than the population
    • The statement the researcher hopes to prove
    • A statement that is always about p > 0.5

  2. The significance level of a test is best described as:

    • The probability of accepting H1 when H1 is true
    • The size of the sample used
    • The probability that H0 is true
    • The probability of rejecting H0 when H0 is true

  3. A 1-tail test is used when the alternative hypothesis states that the parameter is:

    • Not equal to the value in H0
    • Greater than or less than the value in H0
    • Estimated from the sample
    • Equal to the value in H0

  4. A 2-tail test is used when the alternative hypothesis is:

    • p is not equal to p0
    • p is less than p0
    • p is greater than p0
    • p is equal to p0

  5. The critical region of a test is:

    • The set of all possible sample sizes
    • The set of test statistic values that lead to rejecting H0
    • The mean of the sample
    • The set of test statistic values that lead to accepting H0

  6. The p-value of a test is:

    • The significance level chosen before the test
    • The probability, assuming H0 is true, of a result at least as extreme as the one observed
    • The probability that H0 is true
    • The probability of the observed data regardless of H0

  7. If the p-value is less than the significance level, what is the conclusion?

    • Reject H0
    • Accept H0
    • Take a new sample before deciding
    • Prove H1 is true

  8. Why is a sample used to make an inference about a population?

    • Because a sample is always identical to the population
    • Because a sample removes all chance of error
    • Because a sample proves the null hypothesis true
    • Because the sample is used to draw conclusions about the wider population it comes from

  9. The significance level equals the probability of:

    • The test statistic being zero
    • Incorrectly accepting the alternative hypothesis
    • Correctly rejecting H0
    • Incorrectly rejecting the null hypothesis

  10. X ~ B(10, 0.3) under H0 with H1: p < 0.3. Observed X = 0. Which conclusion is correct at the 5% level?

    • The test cannot be done with n = 10
    • Do not reject H0, since 0 is less than the expected value 3
    • Reject H0, since the p-value P(X <= 0) = 0.0282 is less than 0.05
    • Reject H0 at 1%, since 0.0282 is less than 0.01

  11. X ~ B(10, 0.3) under H0 with H1: p < 0.3. Observed X = 1. What is the conclusion at the 5% level?

    • Do not reject H0, since the p-value P(X <= 1) = 0.149 exceeds 0.05
    • Reject H0 at 5%, since 0.149 is below 0.2
    • Reject H0, since 1 is less than the expected value 3
    • Accept H1, since 0.149 is a probability

  12. X ~ B(20, 0.5) under H0 with a 2-tail test at 5%. Observed X = 15. What is the conclusion?

    • Reject H0, since the two-tail p-value is about 0.041, below 0.05
    • Do not reject H0, since the p-value is about 0.5
    • Reject H0, since the two-tail p-value is about 0.207
    • Do not reject H0, since the two-tail p-value is about 0.021

  13. A test at the 5% level finds evidence that the proportion of defective items has decreased. Which conclusion is correct in context?

    • The defect rate is exactly the null value
    • The defect rate has definitely decreased
    • The test proves the defect rate is 0.05
    • There is sufficient evidence at the 5% level that the defect rate has decreased

  14. A test gives a p-value of 0.03 under H0. What does this tell us about the probability that H0 is true?

    • H0 is true with probability 0.97
    • The test does not give the probability that H0 is true
    • H0 is true with probability 0.05
    • The probability that H0 is true is 0.03

  15. X ~ B(10, 0.3) under H0 with H1: p < 0.3 at the 5% level. Which describes the critical region?

    • {7, 8, 9, 10}, since these values are large
    • {0, 1, 2}, since P(X <= 2) is below 0.5
    • {0, 1}, since P(X <= 1) is less than 0.5
    • {0}, since P(X <= 0) = 0.0282 is at most 0.05 but P(X <= 1) = 0.149 is above 0.05

  16. X ~ B(20, 0.5) under H0 with a 2-tail test at 5%. Observed X = 6. What is the conclusion?

    • Reject H0, since the p-value is about 0.058, below 0.05
    • Reject H1, since the p-value is about 0.577
    • Do not reject H0, since the two-tail p-value is about 0.115, above 0.05
    • Accept H1, since 6 is below 10

  17. In a test of a binomial proportion, what is the Type I error probability?

    • The probability of accepting H0 when H1 is true
    • One minus the p-value
    • The power of the test
    • The significance level

  18. For a test of a binomial proportion with X ~ B(n, p0) under H0, which test statistic is used?

    • The sample mean referred to N(p0, 1)
    • X, the number of successes, referred to the binomial distribution under H0
    • The p-value itself
    • The difference between two sample means

  19. A test gives a p-value of 0.04. The same data are tested at the 1% level. What is the conclusion?

    • Do not reject H0 at 1%, since 0.04 is greater than 0.01
    • Reject H0 at 1%, since 0.04 is greater than 0.01
    • Accept H1 at 1%, since 0.04 is positive
    • Reject H0 at 1%, since 0.04 is less than 0.1

  20. A test for a correlation coefficient gives a p-value of 0.02 at the 5% level for a positive correlation. What does this suggest?

    • The variables are causally linked
    • There is evidence at the 5% level of a linear correlation between the variables in the population
    • The correlation coefficient is exactly 0.02
    • There is no evidence of any association at the 5% level

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