Question 1

A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories, and a chi-square test for independence is used to examine the distribution of individuals across the six categories in a 2×3 matrix of categories.Which test has the larger value for df?

Accepted Answer

A)  the test for goodness of fit
B)  the test for independence
C)  Both tests have the same df value.
D)  The df value depends on the sizes of the samples that are used.

Question 2

A chi-square test for independence has df = 2.What is the total number of categories (cells in the matrix)  that were used to classify individuals in the sample?

Accepted Answer

A)  2
B)  3
C)  4
D)  6

Question 3

What happens to the critical value for a chi-square test if the number of categories is increased?

Accepted Answer

A)  The critical value also increases.
B)  The critical value decreases.
C)  The critical value depends on the sample size, not the number of categories.
D)  The critical value is determined entirely by the alpha level.

Question 4

For the chi-square test for goodness-of-fit, the researcher must select a sample with an equal number of individuals in each category.

Accepted Answer

A) True 
 B)False

Question 5

Under what circumstances will the chi-square test for goodness of fit produce a large value for chi-square?

Accepted Answer

A)  when the sample proportions match the hypothesized population proportions
B)  when the sample proportions are much different than the hypothesized population proportions
C)  when the sample mean is close to the population mean
D)  when there is a large difference between the sample mean and the population mean

Question 6

Which of the following is a basic assumption for a chi-square hypothesis test?

Accepted Answer

A)  The population distribution(s)  must be normal.
B)  The scores must come from an interval or ratio scale.
C)  The observations must be independent.
D)  All of the other choices are assumptions for chi-square.

Question 7

The expected frequencies for a chi-square test are always whole numbers (no fractions or decimals).

Accepted Answer

A) True 
 B)False

Question 8

What is referred to by the term observed frequencies?

Accepted Answer

A)  the frequencies found in the sample data
B)  the frequencies found in the population being examined
C)  the frequencies computed from the null hypothesis
D)  the frequencies that are hypothesized for the population being examined

Question 9

In general, a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

Accepted Answer

A) True 
 B)False  False

Question 10

Under what circumstances should the chi-square statistic not be used?

Accepted Answer

A)  if fe > 5 for any cell
B)  if fe 
C)  if fe = fo for any cell
D)  None of the other options is correct.

Question 11

For a fixed level of significance, the critical value for chi-square increases as the degrees of freedom increase.

Accepted Answer

A) True 
 B)False

Question 12

A large value for the chi-square statistic indicates a large discrepancy between the sample data and the hypothesis.

Accepted Answer

A) True 
 B)False

Question 13

What values are specified by the null hypothesis for the chi-square test for goodness of fit?

Accepted Answer

A)  proportions for the entire population.
B)  proportions for the sample.
C)  frequencies for the entire population.
D)  frequencies for the sample.

Question 14

For either chi-square test, Σfe = Σfo.

Accepted Answer

A) True 
 B)False  True

Question 15

Which of the following accurately describes the chi-square test for independence?

Accepted Answer

A)  It is similar to a single-sample t test because it uses one sample to test a hypothesis about one population.
B)  It is similar to a correlation because it uses one sample to evaluate the relationship between two variables.
C)  It is similar to an independent-measures t test because it uses separate samples to evaluate the difference between separate populations.
D)  It is similar to both a correlation and an independent-measures t test because it can be used to evaluate a relationship between variables or a difference between populations. D

Question 16

The data for a chi-square test for independence can be viewed either as representing one sample with two measurements for each participant or as two (or more) separate samples.

Accepted Answer

A) True 
 B)False

Question 17

A researcher obtains a negative value for chi-square statistic.What can you conclude because the value is negative?

Accepted Answer

A)  The observed frequencies are consistently larger than the expected frequencies.
B)  The expected frequencies are consistently larger than the observed frequencies.
C)  There are large differences between the observed and expected frequencies.
D)  The researcher made a mistake.The value of chi-square cannot be negative.

Question 18

What is referred to by the term expected frequencies?

Accepted Answer

A)  the frequencies found in the sample data
B)  the frequencies found in the population being examined
C)  the frequencies computed from the null hypothesis
D)  the frequencies that are hypothesized for the population being examined

Question 19

In a chi-square test for independence or goodness of fit _____.

Accepted Answer

A)  Σfe = n
B)  Σfe = Σfo
C)  both Σfe = n and Σfe = Σfo
D)  neither Σfe = n nor Σfe = Σfo

Question 20

The degrees of freedom for a chi-square test are not related to the size of the sample.

Accepted Answer

A) True 
 B)False

Exam 17: Chi-Square Tests

A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories, and a chi-square test for independence is used to examine the distribution of individuals across the six categories in a 2×3 matrix of categories.Which test has the larger value for df?

Correct AnswerverifiedShow Answer

A chi-square test for independence has df = 2.What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?

Correct AnswerverifiedShow Answer

What happens to the critical value for a chi-square test if the number of categories is increased?

Correct AnswerverifiedShow Answer

For the chi-square test for goodness-of-fit, the researcher must select a sample with an equal number of individuals in each category.

Correct AnswerverifiedShow Answer

Under what circumstances will the chi-square test for goodness of fit produce a large value for chi-square?

Correct AnswerverifiedShow Answer

Which of the following is a basic assumption for a chi-square hypothesis test?

Correct AnswerverifiedShow Answer

The expected frequencies for a chi-square test are always whole numbers (no fractions or decimals).

Correct AnswerverifiedShow Answer

What is referred to by the term observed frequencies?

Correct AnswerverifiedShow Answer

In general, a large value for chi-square indicates a good fit between the sample data and the null hypothesis.

Correct AnswerverifiedFalse

Under what circumstances should the chi-square statistic not be used?

Correct AnswerverifiedShow Answer

For a fixed level of significance, the critical value for chi-square increases as the degrees of freedom increase.

Correct AnswerverifiedShow Answer

A large value for the chi-square statistic indicates a large discrepancy between the sample data and the hypothesis.

Correct AnswerverifiedShow Answer

What values are specified by the null hypothesis for the chi-square test for goodness of fit?

Correct AnswerverifiedShow Answer

For either chi-square test, Σfe = Σfo.

Correct AnswerverifiedTrue

Which of the following accurately describes the chi-square test for independence?

Correct AnswerverifiedD

The data for a chi-square test for independence can be viewed either as representing one sample with two measurements for each participant or as two (or more) separate samples.

Correct AnswerverifiedShow Answer

A researcher obtains a negative value for chi-square statistic.What can you conclude because the value is negative?

Correct AnswerverifiedShow Answer

What is referred to by the term expected frequencies?

Correct AnswerverifiedShow Answer

In a chi-square test for independence or goodness of fit _____.

Correct AnswerverifiedShow Answer

The degrees of freedom for a chi-square test are not related to the size of the sample.

Correct AnswerverifiedShow Answer

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False

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For either chi-square test, Σf_e = Σf_o.

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True

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D

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