Question 1

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.

Accepted Answer

A) True 
 B)False

Question 2

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

Accepted Answer

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 3

A researcher is interested in consumer preferences among three brands of yogurt.A sample of 90 people is obtained,and each individual is asked to taste each brand and then select his/her favorite.The resulting frequency data are as follows:
 $$\begin{array} { | c | c | c | } 
\hline \text { Brand A } &{ \text { Brand B } } & \text { Brand C } \
\hline 37 & 21 & 32 \
\hline
\end{array}$$ 
Do the data indicate any significant preferences among the three brands? Test at the .05 level of significance.

Accepted Answer

The answer of A researcher is interested in consumer preferences...

Question 4

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) 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 5

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

Accepted Answer

A) True 
 B)False

Question 6

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?

Accepted Answer

A) 10 
B) 20 
C) 40 
D) 100

Question 7

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.

Question 8

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 9

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?

Accepted Answer

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

Question 10

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?

Accepted Answer

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

Question 11

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?

Accepted Answer

A) Greater than 7.81 
B) Less than 7.81 
C) Greater than 79.08 
D) Less than 79.08

Question 12

A researcher is examining preferences among four new flavors of ice cream.A sample of n = 80 people is obtained.Each person tastes all four flavors and then picks his/her favorite.The distribution of preferences is as follows.
 $$\begin{array} { l } 
\text { Ice Cream Flavor } \
\begin{array} { | c | c | c | c | } 
\hline \text { A }& \text { B } & \text { C } & \text { D } \
\hline & & & \
12 & 18 & 28 & 22 \
\hline
\end{array}
\end{array}$$ 
Do these data indicate any significant preferences among the four flavors? Test at the .05 level of significance.

Accepted Answer

The answer of A researcher is examining preferences among four...

Question 13

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

Accepted Answer

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 14

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.

Accepted Answer

A) True 
 B)False

Question 15

A researcher is interested in the relationship between birth order and personality.A sample of n = 100 people is obtained,all of whom grew up in families as one of three children.Each person is given a personality test,and the researcher also records the person's birth-order position (1st born,2nd,or 3rd).The frequencies from this study are shown in the following table.On the basis of these data,can the researcher conclude that there is a significant relation between birth order and personality? Test at the .05 level of significance.

Accepted Answer

The answer of A researcher is interested in the relationship...

Question 16

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 17

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 18

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?

Accepted Answer

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

Question 19

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?

Accepted Answer

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

Question 20

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?

Accepted Answer

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.

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

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.

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

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

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

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

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?

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

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.

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

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

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 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 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?