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Test for Homogeneity Quiz

12 questions math Grades 9-12

The question sheet

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  1. Which test decides whether two populations follow the same unknown distribution?

    • Goodness-of-fit test
    • Test for homogeneity
    • Test of independence
    • Correlation test
    Reveal answer

    Answer: Test for homogeneity

    Source evidence

    PDF page 612: The goodness-of-fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to draw a conclusion about whether two populations have the same distribution. To calculate

  2. The goodness-of-fit test is NOT sufficient to decide whether:

    • Two populations follow same distribution
    • Data are categorical
    • A population fits a distribution
    • Expected values are large
    Reveal answer

    Answer: Two populations follow same distribution

    Source evidence

    PDF page 612: The goodness-of-fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to draw a conclusion about whether two populations have the same distribution. To calculate

  3. To calculate the test statistic for homogeneity, you follow the same procedure as the:

    • Test of independence
    • Goodness-of-fit test
    • ANOVA test
    • Correlation test
    Reveal answer

    Answer: Test of independence

    Source evidence

    PDF page 613: the test statistic for a test for homogeneity, follow the same procedure as with the test of independence.

  4. The alternative hypothesis for a test for homogeneity states the distributions are:

    • Normal
    • Independent
    • Equal
    • Not the same
    Reveal answer

    Answer: Not the same

    Source evidence

    PDF page 613: Ha: The distributions of the two populations are not the same. Test Statistic Use a test statistic. It is computed in the same way as the test for independence. Degrees of freedom (df) df = (number of columns – 1)(number of rows – 1) Requirements All values in the table must be greater than or equal to five. Common Uses Comparing two populations. For example: men vs. women, before vs. after, east vs. west. The variable is categorical with more than two possible response values.

  5. Degrees of freedom for a test for homogeneity equal:

    • (columns – 1)(rows – 1)
    • columns + rows – 2
    • number of cells – 1
    • rows × columns
    Reveal answer

    Answer: (columns – 1)(rows – 1)

    Source evidence

    PDF page 613: Ha: The distributions of the two populations are not the same. Test Statistic Use a test statistic. It is computed in the same way as the test for independence. Degrees of freedom (df) df = (number of columns – 1)(number of rows – 1) Requirements All values in the table must be greater than or equal to five. Common Uses Comparing two populations. For example: men vs. women, before vs. after, east vs. west. The variable is categorical with more than two possible response values.

  6. In the living arrangements example, the degrees of freedom equaled:

    • 3
    • 6
    • 2
    • 4
    Reveal answer

    Answer: 3

    Source evidence

    PDF page 613: df = (number of columns – 1)(number of rows – 1) = (4 – 1)(2– 1) = 3

  7. In the living arrangements example, the test statistic χ² was:

    • 0.0175
    • 3.2603
    • 10.1287
    • 0.1959
    Reveal answer

    Answer: 10.1287

    Source evidence

    PDF page 613: 2 Calculate the test statistic: χ = 10.1287 (calculator or computer)

  8. In the living arrangements example, the p-value was:

    • 0.05
    • 10.1287
    • 0.1959
    • 0.0175
    Reveal answer

    Answer: 0.0175

    Source evidence

    PDF page 613: Probability statement: p-value = P(χ >10.1287) = 0.0175

  9. The living arrangements conclusion was that the distributions are:

    • Independent
    • Normal
    • The same
    • Not the same
    Reveal answer

    Answer: Not the same

    Source evidence

    PDF page 615: Conclusion: At a 5 percent level of significance, from the data, there is sufficient evidence to conclude that the distributions of living arrangements for male and female college students are not the same.

  10. According to the text, the homogeneity test can tell us the distributions differ but not:

    • How they differ
    • The test statistic
    • The p-value
    • The df
    Reveal answer

    Answer: How they differ

    Source evidence

    PDF page 615: Notice that the conclusion is only that the distributions are not the same. We cannot use the test for homogeneity to draw any conclusions about how they differ.

  11. In the voter preferences example, the degrees of freedom equaled:

    • 4
    • 2
    • 3
    • 1
    Reveal answer

    Answer: 2

    Source evidence

    PDF page 616: df = (number of columns – 1)(number of rows – 1) = (3 – 1)(2 – 1) = 2

  12. In the voter preferences example, the test statistic χ² was:

    • 0.0175
    • 3.2603
    • 10.1287
    • 0.1959
    Reveal answer

    Answer: 3.2603

    Source evidence

    PDF page 616: 2 Calculate the test statistic: χ = 3.2603 (calculator or computer)

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Source

Statistics

Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.

Original textbook · CC BY 4.0

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