Deck 17: Chi-Square Tests

Question 1

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

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.

Answer 1

D

Question 2

A chi-square test for goodness of fit has df = 2.How many categories were used to classify the individuals in the sample?

A)2
B)3
C)4
D)cannot be determined without additional information

Answer 2

B

Question 3

Which of the following accurately describes the chi?square distribution?

A)symmetrical with a mean of zero
B)positively skewed with all values greater than or equal to zero
C)negatively skewed with all values greater than or equal to zero
D)symmetrical with a mean equal to n - 1

Answer 3

B

Question 4

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

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

Question 5

Which of the following accurately describes the observed frequencies for a chi-square test?

A)They are always whole numbers.
B)They can contain fractions or decimal values.
C)They can contain both positive and negative values.
D)They can contain fractions and negative numbers.

Question 6

Which of the following best describes the possible values for a chi-square statistic?

A)Chi-square is always a positive whole numbers.
B)Chi-square is always positive but can contain fractions or decimal values.
C)Chi-square can be either positive or negative, but always is a whole number.
D)Chi-square can be either positive or negative and can contain fractions or decimals.

Question 7

A sample of n = 100 people is classified into four categories.If the results are evaluated with a chi-square test for goodness of fit, what is the df value for the chi-square statistic?

A)3
B)4
C)99
D)100

Question 8

How does the difference between f_e and f_o influence the outcome of a chi-square test?

A)The larger the difference, the larger the value of chi-square and the greater the likelihood of rejecting the null hypothesis.
B)The larger the difference, the larger the value of chi-square and the lower the likelihood of rejecting the null hypothesis.
C)The larger the difference, the smaller the value of chi-square and the greater the likelihood of rejecting the null hypothesis.
D)The larger the difference, the smaller the value of chi-square and the lower the likelihood of rejecting the null hypothesis.

Question 9

A researcher used a sample of n = 60 individuals to determine whether there are any preferences among four brands of pizza.Each individual tastes all four brands and selects his/her favorite.If the data are evaluated with a chi-square test for goodness of fit using α = .05, then how large does the chi-square statistic need to be to reject the null hypothesis?

A)greater than 7.81.
B)less than 7.81.
C)greater than 79.08.
D)less than 79.08.

Question 10

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

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.

Question 11

Which of the following accurately describes the expected frequencies for a chi-square test?

A)They are always whole numbers.
B)They can contain fractions or decimal values.
C)They can contain both positive and negative values.
D)They can contain fractions and negative numbers.

Question 12

Ten years ago, only 15% of the U.S.population consisted of people more than 65 years old.A researcher plans to use a sample of n = 300 people to determine whether the population distribution has changed during the past ten years.If a chi-square test is used to evaluate the data, what is the expected frequency for the older-than-65 category?

A)15
B)30
C)45
D)150

Question 13

What is referred to by the term observed frequencies?

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 14

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

A)There is a good fit between the sample data and the null hypothesis.
B)There is a large discrepancy between the sample data and the null hypothesis.
C)All of the expected frequencies must also be close to zero.
D)The researcher made a mistake because chi-square can never be close to zero.

Question 15

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

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.

Question 16

What is indicated by a large value for the chi-square statistic?

A)The sample data (observed values) do not match the null hypothesis.
B)There is a good fit between the sample data (observed values) and the null hypothesis.
C)The observed values from the sample data are consistently larger than the expected values.
D)The observed values from the sample data are consistently smaller than the expected values.

Question 17

For a fixed level of significance, the critical value for chi-square will ______.

A)increase as the df value increases.
B)decrease as the df value increases.
C)increase as the sample size increases.
D)decrease as the sample size increases.

Question 18

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

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

Question 19

What is referred to by the term expected frequencies?

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 20

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

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 21

What is evaluated by the chi-square test for goodness of fit?

A)the relationship between two variables
B)the mean differences between two or more treatments
C)the shape or proportions for a population distribution
D)None of the other options are evaluated by the chi-square test.

Question 22

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

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 23

When the data form a 2x2 matrix, the phi-coefficient is used to measure effect size for the chi-square test for independence.If other factors are held constant, how does sample size influence the values for phi and chi-square?

A)A larger sample increase both phi and chi-square.
B)A larger sample increases phi but has no effect on chi-square.
C)A larger sample increases chi-square but has no effect on phi.
D)Sample size does not influence either phi or chi-square.

Question 24

How do you compute df for the chi-square test for goodness of fit?

A)df = n - 1
B)df = n - 2
C)df = n - C (where C is the number of categories)
D)None of the other 3 choices is correct.

Question 25

A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile.Each individual in a sample of n = 30 males and n = 30 females selects a favorite design from the three choices.If the researcher obtains a chi-square statistic of χ² = 4.81, what is the appropriate statistical decision for the test?

A)Reject the null hypothesis with α = .05 but not with α = .01.
B)Reject the null hypothesis with either α = .05 or α = .01.
C)Fail to reject the null hypothesis with either α = .05 or α = .01.
D)There is not enough information to determine the appropriate decision.

Question 26

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

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 27

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

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 28

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?

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

Question 29

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

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

Question 30

A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters.The sample consists of 80 females and 20 males, and has a total of 60 registered voters.If these data were used for a chi-square test for independence, what is the expected frequency for males who are registered voters?

A)12
B)20
C)40
D)cannot determine without additional information

Question 31

A chi-square test for independence is used to evaluate the relationship between two variables.If both variables are classified into 2 categories, then what is the df value for the chi-square statistic?

A)df = 1
B)df = 2
C)df = 3
D)cannot determine the value of df from the information provided

Question 32

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

A)Σf_e = n
B)Σf_e = Σf_o
C)both Σf_e = n and Σf_e = Σf_o
D)neither Σf_e = n nor Σf_e = Σf_o

Question 33

Under what conditions is Cramér's V used to measure effect size for a chi-square test for independence?

A)When both variables consist of exactly two categories
B)When both variables consist of more than two categories
C)When either of the two variables consists of exactly two categories
D)When either of the two variables consists of more than two categories

Question 34

A sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters.The sample consists of 80 females and 20 males, and has a total of 60 registered voters.If these data are used for a chi-square test for independence, what is the total number of females for the expected frequencies?

A)32
B)20
C)48
D)80

Question 35

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?

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 36

What is stated by the null hypothesis for the chi-square test for independence?

A)There is a relationship between the two variables.
B)There is no relationship between the two variables.
C)Both variables have the same frequency distribution.
D)The two variables have different frequency distributions.

Question 37

A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories.The chi-square statistic for this test would have df equal to ______.

A)6
B)7
C)10
D)11

Question 38

A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote.The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters.If these data were used for a chi-square test for independence, what is the observed frequency for registered males?

A)12
B)28
C)40
D)42

Question 39

A chi-square test for independence has df = 3.What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?

A)4
B)6
C)8
D)9

Question 40

A researcher selects a sample of 100 people to investigate the relationship between gender (male/female) and registering to vote.The sample consists of 40 females, of whom 30 are registered voters, and 60 males, of whom 40 are registered voters.If these data were used for a chi-square test for independence, what is the expected frequency for registered females?

A)12
B)28
C)40
D)42

Question 41

The data for a chi-square test are called observed frequencies.

Question 42

For a chi-square test, the expected frequencies are calculated values that are intended to produce a sample that is representative of the null hypothesis.

Question 43

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

Question 44

One characteristic of nonparametric tests is that they make few, if any, assumptions about the populations being investigated.

Question 45

It is impossible to obtain a negative value for chi-square.

Question 46

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

Question 47

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

Question 48

The phi-coefficient is used to evaluate effect size for a chi-square test for goodness of fit provided there are only two categories.

Question 49

For either chi-square test, Σf_e = n.

Question 50

The chi-square test for independence uses the same formula as the chi-square statistic for the goodness-of-fit test.

Question 51

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

Question 52

A chi-square test for independence produces a chi-square statistic with df = 2.The data for this research study form a matrix with four separate categories.

Question 53

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

Question 54

One characteristic of the chi-square tests is that they can be used when the data are measured on a nominal scale.

Question 55

For a fixed level of significance, the critical value for chi-square increases as the size of the sample increases.

Question 56

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

Question 57

The chi-square distribution tends to be symmetrical with a mean of μ = 0.

Question 58

For a chi-square test, the observed frequencies are obtained from the sample.

Question 59

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

Question 60

For either chi-square test, Σf_e = Σf_o.

Question 61

The chi-square test for independence is similar to an independent-measures t test because it can be used to evaluate the difference between two populations or two treatment conditions.

Question 62

For a chi-square test for independence, the expected frequencies for any row are exactly the same as the expected frequencies in every other row.

Question 63

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.

Question 64

The chi-square test for goodness of fit evaluates the distribution for one variable, and the test for independence evaluates the relationship between two variables.

Question 65

The phi-coefficient is used to evaluate effect size for the chi-square test for independence, provided the test has df = 1.

Question 66

A chi?square test should not be used if any expected frequency is less than five.

Question 67

Although the outcome for a chi-square test for independence is influenced by sample size, measures of effect size such as the phi-coefficient or Cramér's V are not.

Question 68

Cramér's V is used to evaluate effect size for the chi-square test for independence whenever the test has df > 1.

Question 69

If other factors are held constant, increasing the sample size for a chi-square test for independence will increase the likelihood of rejecting the null hypothesis.

Question 70

The chi-square test for independence is similar to a correlation because it evaluates the relationship between two variables.