Deck 15: The Chi-Square Statistic: Tests for Goodness of Fit and Independence

Question 1

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 1

3

Question 2

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 2

Positively skewed with all values greater than or equal to zero

Question 3

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 3

The researcher made a mistake; the value of chi-square cannot be negative.

Question 4

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 5

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 6

How does the difference between fₑ and fₒ 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 7

For a fixed level of significance,how is the critical value for chi-square related to degrees of freedom?

A)The critical value increases as df increases.
B)The critical value decreases as df increases.
C)The critical value increases as sample size increases.
D)The critical value decreases as sample size increases.

Question 8

Ten years ago,only 20% of the U.S.population consisted of people more than 65 years old.A researcher plans to use a sample of n = 200 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)10
B)20
C)40
D)100

Question 9

What happens to the shape of the chi-square distribution as the df value increases?

A)The mode (highest point) of the distribution moves to the right.
B)The mode (highest point) of the distribution moves to the left.
C)The mode (highest point) of the distribution does not move, but the distribution becomes more spread out.
D)The mode (highest point) of the distribution does not move, but the distribution becomes more tightly clustered around the mode.

Question 10

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 11

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

A)The critical value 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 12

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 13

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

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

Question 14

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 15

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 16

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

A)The critical value 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 17

The data for a chi-square test consist of ___________.

A)numerical scores
B)non-numerical categories
C)ranks
D)frequencies

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 values are specified by the null hypothesis for a chi-square test?

A)Frequencies for a sample
B)Frequencies for a population
C)Proportions for a sample
D)Proportions for a population

Question 20

A researcher is using a chi-square test to determine whether people have any preferences among three brands of televisions.The null hypothesis for this test would state that ______.

A)there are real preferences in the population
B)one-third of the sample prefers each brand
C)one-third of the population prefers each brand
D)in the population, one brand is preferred over the other two

Question 21

A researcher is using a chi-square test for independence to evaluate the relationship between birth-order position and self-esteem.Each individual is classified as being 1ˢᵗ born,2ⁿᵈ born,or 3ʳᵈ born,and self-esteem is categorized as either high or low.For this study,what is the df value for the chi-square statistic?

A)1
B)2
C)3
D)4

Question 22

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)1
B)2
C)3
D)Cannot determine the value of df from the information provided

Question 23

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 24

In the observed frequencies for a chi-square test for independence,how often is each participant counted?

A)Just once
B)Once in each row
C)Once in each column
D)Once in each row and once in each column

Question 25

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.What is the df value for the chi-square statistic?

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

Question 26

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 27

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 28

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.
D)The df value depends on the sizes of the samples that are used.

Question 29

A researcher used a sample of n = 50 individuals to determine whether they are any preferences between two new designs for a smart phone.If the data produce a chi-square statistic of χ² = 6.00 what decision should the researcher make?

A)There is a significant preference at both α = .05 and α = .01.
B)There is a significant preference at α = .05 but not at α = .01.
C)There is no significant preference at either α = .05 or α = .01.
D)There is no significant preference at α = .05 but there is at α = .01.

Question 30

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 31

Which of the following is always true for a chi-square test for goodness of fit or a test for independence?

A)Σfe = n
B)Σfe = Σfo
C)Both Σfe = n and Σfe = Σfo
D)Neither Σfe = n nor Σfe = Σfo

Question 32

A sample of 100 people is classified by gender (male/female)and by whether 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 33

Under what circumstances will the chi-square test for goodness of fit produce a large value for the 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 34

A researcher would like to test the claim that 9 out of 10 doctors prefer Brand X.A sample of 60 doctors is obtained and each is asked to compare Brand X with another leading brand.The data show that 48 of the doctors picked Brand X.If these data are evaluated using a chi-square test for goodness of fit,what is the expected frequency for Brand X?

A)6
B)12
C)48
D)54

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 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 37

A sample of 100 people is classified by gender (male/female)and by whether 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 38

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 39

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 40

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 2×3 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.
D)The df value depends on the sizes of the samples that are used.

Question 41

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 42

Nonparametric tests are used only with data from a nominal scale.

Question 43

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

A)The population distribution(s) must be normal.
B)All scores 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 44

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

Question 45

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

Question 46

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

Question 47

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

Question 48

A chi-square test for independence is being used to evaluate the relationship between two variables.If the test has df = 1,what can you conclude about the two variables?

A)One variable consists of 2 categories and the other consists of 3 categories.
B)One variable consists of 2 categories and the other consists of 4 categories.
C)Both variables consist of 2 categories.
D)Both variables consist of 3 categories.

Question 49

A chi-square test for independence is being used to evaluate the relationship between two variables.If the test has df = 3,what can you conclude about the two variables?

A)One variable consists of 2 categories and the other consists of 3 categories.
B)One variable consists of 2 categories and the other consists of 4 categories.
C)Both variables consists of 2 categories.
D)Both variables consists of 3 categories.

Question 50

Chi-square values are always greater than or equal to zero.

Question 51

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

Question 52

When the data form a 2×2 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 increases 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 53

For either chi-square test,Σfₑ = n.

Question 54

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

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

Question 55

A chi-square test for independence is being used to evaluate the relationship between two variables.If the test has df = 2,what can you conclude about the two variables?

A)One variable consists of 2 categories and the other consists of 3 categories.
B)One variable consists of 2 categories and the other consists of 4 categories.
C)Both variables consist of 2 categories.
D)Both variables consist of 3 categories.

Question 56

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 57

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 58

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 59

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

Question 60

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 61

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 62

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

Question 63

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

Question 64

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 65

The observed frequencies for a chi-square test can be fractions or decimal values.

Question 66

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

Question 67

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

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

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

Question 70

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 71

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 72

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

Question 73

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

Question 74

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

Question 75

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 76

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

Question 77

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 78

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

Question 79

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 80

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