Test for Homogeneity Quiz
The question sheet
Reveal any answer as you study-
Which test decides whether two populations follow the same unknown distribution?
- Goodness-of-fit test
- Regression test
- Test of proportion
- Test for homogeneity
Reveal answer
Answer: Test for homogeneity
Source evidence
PDF page 662: 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 the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. NOTE The expected value for each cell needs to be at least five for you to use this test.
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How is the test statistic for a test for homogeneity calculated?
- Same as goodness-of-fit
- Using an F ratio
- Using a z-score
- Same as test of independence
Reveal answer
Answer: Same as test of independence
Source evidence
PDF page 662: 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 the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. NOTE The expected value for each cell needs to be at least five for you to use this test.
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What is the null hypothesis for a test for homogeneity?
- Populations differ in size
- Distributions are not the same
- Distributions are the same
- Means are equal
Reveal answer
Answer: Distributions are the same
Source evidence
PDF page 662: H0: The distributions of the two populations are the same.
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Which test statistic is used in a test for homogeneity?
- z statistic
- F statistic
- t statistic
- χ² statistic
Reveal answer
Answer: χ² statistic
Source evidence
PDF page 662: Ha: The distributions of the two populations are not the same. Test Statistic 2 Use a χ test statistic. It is computed in the same way as the test for independence. Degrees of freedom (df) df = number of columns – 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.
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How are the degrees of freedom found in a test for homogeneity?
- number of columns – 1
- number of rows – 1
- number of cells – 1
- (rows-1)(cols-1)
Reveal answer
Answer: number of columns – 1
Source evidence
PDF page 662: Ha: The distributions of the two populations are not the same. Test Statistic 2 Use a χ test statistic. It is computed in the same way as the test for independence. Degrees of freedom (df) df = number of columns – 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.
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What minimum expected value must each cell have to use this test?
- At least one
- At least five
- At least twenty
- At least ten
Reveal answer
Answer: At least five
Source evidence
PDF page 662: 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 the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. NOTE The expected value for each cell needs to be at least five for you to use this test.
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Which is a common use of the test for homogeneity?
- Comparing two populations
- Estimating a mean
- Testing correlation
- Predicting a value
Reveal answer
Answer: Comparing two populations
Source evidence
PDF page 662: Ha: The distributions of the two populations are not the same. Test Statistic 2 Use a χ test statistic. It is computed in the same way as the test for independence. Degrees of freedom (df) df = number of columns – 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.
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In the living arrangements example, what were the degrees of freedom?
- 6
- 2
- 4
- 3
Reveal answer
Answer: 3
Source evidence
PDF page 663: df = number of columns – 1 = 4 – 1 = 3
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What was the test statistic in the living arrangements example?
- 10.1287
- 0.0175
- 3.2603
- 0.1959
Reveal answer
Answer: 10.1287
Source evidence
PDF page 663: Calculate the test statistic: χ = 10.1287 (calculator or computer)
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What was the p-value in the living arrangements example?
- 10.1287
- 0.1959
- 0.05
- 0.0175
Reveal answer
Answer: 0.0175
Source evidence
PDF page 663: Probability statement: p-value = P(χ >10.1287) = 0.0175
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What decision was made in the living arrangements example?
- No conclusion possible
- Accept Ha only partly
- Do not reject H0
- Reject H0
Reveal answer
Answer: Reject H0
Source evidence
PDF page 663: Make a decision: Since α > p-value, reject H0. This means that the distributions are not the same.
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In the living arrangements example, why was H0 rejected?
- α > p-value
- α equals p-value
- p-value > α
- df was too small
Reveal answer
Answer: α > p-value
Source evidence
PDF page 663: Compare α and the p-value: Since no α is given, assume α = 0.05. p-value = 0.0175. α > p-value.
PDF page 663: Make a decision: Since α > p-value, reject H0. This means that the distributions are not the same.
High School Statistics
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