Goodness-of-Fit Test Quiz
The question sheet
Reveal any answer as you study-
Which distribution is used for the goodness-of-fit hypothesis test?
- Chi-square
- Normal
- Student's t
- Uniform
Reveal answer
Answer: Chi-square
Source evidence
PDF page 599: In this type of hypothesis test, you determine whether the data fit a particular distribution. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test, meaning the distribution for the hypothesis test is chi-square, to determine if there is a fit. The null and the alternative hypotheses for this test may be written in sentences or may be stated as equations or inequalities. The test statistic for a goodness-of-fit test is:
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In the test statistic, what does O represent?
- Odds ratio
- Observed values (data)
- Number of categories
- Expected values
Reveal answer
Answer: Observed values (data)
Source evidence
PDF page 599: • O = observed values (data),
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In the goodness-of-fit test statistic, what does E represent?
- Estimated error
- Extreme values
- Expected values from theory
- Empirical frequency
Reveal answer
Answer: Expected values from theory
Source evidence
PDF page 599: • E = expected values (from theory), and
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How is the number of degrees of freedom calculated?
- Sample size – 1
- Number of categories
- Number of categories + 1
- Number of categories – 1
Reveal answer
Answer: Number of categories – 1
Source evidence
PDF page 599: The number of degrees of freedom is df = (number of categories – 1). The goodness-of-fit test is almost always right-tailed. If the observed values and the corresponding expected values are not close to each other, then the test statistic can get very large and will be way out in the right tail of the chi-square curve.
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The goodness-of-fit test is almost always:
- Two-tailed
- Left-tailed
- Right-tailed
- Non-directional
Reveal answer
Answer: Right-tailed
Source evidence
PDF page 599: The number of degrees of freedom is df = (number of categories – 1). The goodness-of-fit test is almost always right-tailed. If the observed values and the corresponding expected values are not close to each other, then the test statistic can get very large and will be way out in the right tail of the chi-square curve.
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What is the minimum expected value for each cell to use this test?
- At least thirty
- At least one
- At least five
- At least ten
Reveal answer
Answer: At least five
Source evidence
PDF page 599: The expected value for each cell needs to be at least five for you to use this test.
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What are the expected values in a goodness-of-fit test?
- Values expected if H0 were true
- The largest data values
- Randomly chosen values
- Values from the alternative
Reveal answer
Answer: Values expected if H0 were true
Source evidence
PDF page 599: The observed values are the data values, and the expected values are the values you would expect to get if the null hypothesis were true. There are n terms of the form .
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In the absenteeism example, why could the original tables not be used directly?
- Too many categories
- Sample size too small
- Data were continuous
- Expected number for 12+ was under five
Reveal answer
Answer: Expected number for 12+ was under five
Source evidence
PDF page 600: a. No. Notice that the expected number of absences for the 12+ entry is less than five; it is two. Combine that group with
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After combining groups, how many degrees of freedom did the absenteeism test have?
- 4
- 3
- 5
- 2
Reveal answer
Answer: 3
Source evidence
PDF page 601: b. There are four cells or categories in each of the new tables.
PDF page 601: df = number of cells – 1 = 4 – 1 = 3.
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In the employee absence example, the null hypothesis states absent days fit which distribution?
- Binomial
- Uniform
- Normal
- Chi-square
Reveal answer
Answer: Uniform
Source evidence
PDF page 602: • H0: The absent days occur with equal frequencies; that is, they fit a uniform distribution.
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In the employee absence example, what was the chi-square test statistic?
- Five
- Twelve
- Sixty
- Three
Reveal answer
Answer: Three
Source evidence
PDF page 602: 2 Now add (sum) the last column. The sum is three. This is the χ test statistic. 2 To find the p-value, calculate P(χ > 3). This test is right-tailed. Use a computer or calculator to find the p-value. You should get p-value = 0.5578.
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In the employee absence example, the p-value was:
- 0.3430
- 0.9500
- 0.5578
- 0.0006
Reveal answer
Answer: 0.5578
Source evidence
PDF page 602: 2 Now add (sum) the last column. The sum is three. This is the χ test statistic. 2 To find the p-value, calculate P(χ > 3). This test is right-tailed. Use a computer or calculator to find the p-value. You should get p-value = 0.5578.
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