Deck 13: Chi-Square Procedures

Question 1

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
At the 0.01 significance level, do the data provide sufficient evidence to conclude that an
association exists between car color and the likelihood of being in an accident?

Answer 1

Question 2

Provide an appropriate response.
The contingency table below shows political party affiliation cross classified by age group
for a certain population. What information would be given by the conditional distribution
of age group for Democrats? How would you obtain this conditional distribution?

Answer 2

The conditional distribution of age group for Democrats would give the percentage
of Democrats falling in each age group and would be obtained by dividing each of
the numbers in the first row by the total number of Democrats, 117.

Question 3

Perform a chi-square independence test using the P-value approach, provided the conditions for using the test are met.Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to compute the value of thetest statistic, to obtain the P-value, and to state your conclusion.
A car insurance company performed a study to determine whether an association exists
between age and the frequency of car accidents. They obtained the following sample data. At the 5% significance level, do the data provide sufficient evidence to conclude that an
association exists between age and frequency of car accidents?

Answer 3

Question 4

Perform a chi-square independence test using the P-value approach, provided the conditions for using the test are met.Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to compute the value of thetest statistic, to obtain the P-value, and to state your conclusion.
A researcher performed a study to determine whether an association exists between sex
and blood type. He obtained the following sample data. At the 10% significance level, do the data provide sufficient evidence to conclude that an
association exists between sex and blood type?

Question 5

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
The Book Industry Study Group, Inc., performs sample surveys to obtain information on
characteristics of book readers. A book reader is defined to be one who read one or more
books in the six months prior to the survey; a non-book reader is defined to be one who
read newspapers or magazines but no books in the six months prior to the survey; a
nonreader is defined to be one who did not read a book, newspaper, or magazine in the six
months prior to the survey. The following data were obtained from a random sample of
1429 persons 16 years old and over. At the 1% significance level, do the data provide sufficient evidence to conclude that an
association exists between "household income" and "reader classification"?

Question 6

Provide an appropriate response.
What assumptions are made when using a chi-square goodness-of-fit test?

Question 7

Provide an appropriate response.
The table below shows the conditional distributions of the variable blood type for men and
for women for a certain population. Is it possible to determine the marginal distribution of
blood type? If so, what is it? Is it possible to determine the marginal distribution of sex? If
so, what is it?

Question 8

Perform a chi-square homogeneity test, provided the conditions for the test are met. Use the critical-value approach.
A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated,
180 people are vaccinated with a placebo, and 100 people are not vaccinated. Independent
simple random samples were used and the number in each group who later caught the flu
was recorded. The results are given in the table below, showing the test group and flu
status. Use a 5% significance level to test the claim that there is a difference in the distribution of
flu status for the three test groups.

Question 9

Solve the problem.
The table below shows a distribution and the observed frequencies of the values of a
variable from a simple random sample of a population. Perform a chi-square
goodness-of-fit test, at the specified significance level, to decide whether the distribution
of the variable differs from the given distribution.

Question 10

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
A study conducted for New Woman magazine indicates that the number of children
desired by newly-married American couples is distributed as follows. At the 1% significance level, does it appear that the "number of children desired"
distribution of California couples is different from that of the American population as a
whole?

Question 11

Perform a chi-square independence test using the P-value approach, provided the conditions for using the test are met.Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to compute the value of thetest statistic, to obtain the P-value, and to state your conclusion.
Research is conducted regarding the average age at retirement for four career groups. To
test whether there is a relationship between age of retirement and career in these groups,
700 employees, recently retired, are randomly selected. The resulting data are displayed in
the contingency table below. At the 5% significance level, do the data provide sufficient evidence to conclude that an
association exists between age of retirement and career?

Question 12

Solve the problem.
The table below shows a distribution and the observed frequencies of the values of a
variable from a simple random sample of a population. Perform a chi-square
goodness-of-fit test, at the specified significance level, to decide whether the distribution
of the variable differs from the given distribution.

Question 13

Provide an appropriate response.
When performing a chi-square goodness-of-fit test, how are the expected frequencies
obtained?

Question 14

Perform a chi-square homogeneity test, provided the conditions for the test are met. Use the P-value approach.
An independent simple random sample of 400 men and 400 women was asked whether
they planned to attend a concert in the next month. The results are listed below, showing
the concert attendance status by gender. At the 5% significance level, test the claim that a
difference exists in the distribution of concert attendance status among men and women.

Question 15

Provide an appropriate response.
Which of the following is not an assumption for performing a chi-square homogeneity test?

A)All expected frequencies are 1 or greater.
B)At most 20% of the expected frequencies are greater than 5.
C)Samples are random.
D)Samples are independent.

Question 16

Provide an appropriate response.
Explain why a chi-square goodness-of-fit test is always right-tailed.

Question 17

Perform the indicated goodness-of-fit test using the P-value method. Be sure to state the hypotheses and the significancelevel , to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
A die is rolled 180 times and the following data are obtained. Do the data provide sufficient evidence to conclude that the die is loaded (i.e., that the six
numbers are not equally likely)? Perform the hypothesis test at the 1% level of significance.

Question 18

Perform a chi-square homogeneity test, provided the conditions for the test are met. Use the critical-value approach.
At a high school debate tournament, half of the teams were asked to wear suits and ties
and the rest were asked to wear jeans and t-shirts. The results of independent simple
random samples are given in the table below. Test the hypothesis at the 5% significance
level that the differently dressed debate teams are nonhomogeneous with respect to
tournament wins/losses.

Question 19

Perform a chi-square independence test using the P-value approach, provided the conditions for using the test are met.Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to compute the value of thetest statistic, to obtain the P-value, and to state your conclusion.
A researcher performed a study to determine whether an association exists between
political party affiliation and income. She obtained the following sample data. At the 1% significance level, do the data provide sufficient evidence to conclude that an
association exists between political party affiliation and income?

Question 20

Perform a chi-square homogeneity test, provided the conditions for the test are met. Use the critical-value approach.
A researcher wishes to test whether the proportion of college students who smoke is the
same in four different colleges. She uses independent simple random samples to select 100
students from each college and records the number that smoke. The results are shown
below, showing smoking status and college. Use a 1% significance level to test the claim that the distribution of smoking status is
different at the four colleges.

Question 21

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
A car insurance company performed a study to determine whether an association exists
between age and the frequency of car accidents. They obtained the following sample data. At the 1% significance level, do the data provide sufficient evidence to conclude that an
association exists between age and frequency of car accidents?

Question 22

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
The table below shows the age and favorite type of music of 668 randomly selected people. At the 0.05 significance level, do the data provide sufficient evidence to conclude that an
association exists between age and preferred music type?

Question 23

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
Research is conducted regarding the average age at retirement for four career groups. To
test whether there is a relationship between age of retirement and career in these groups,
700 employees, recently retired, are randomly selected. The resulting data are displayed in
the contingency table below. At the 5% significance level, do the data provide sufficient evidence to conclude that an
association exists between age of retirement and career?

Question 24

Provide an appropriate response.
Explain the difference between univariate and bivariate data.

Question 25

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
160 students who were majoring in either math or English were asked a test question, and
the researcher recorded whether they answered the question correctly. The sample results
are given below. At the 0.10 significance level, do the data provide sufficient evidence to
conclude that an association exists between response and major?

Question 26

Provide an appropriate response.
What is a chi-square goodness-of-fit test used for? For what kinds of variable can it be
used?

Question 27

Provide an appropriate response.
Suppose that you wish to perform a chi-square test of independence. The two variables
under consideration are sex and blood type. True or false, if the two variables are not
associated, we would expect that in the sample, the number of women with a given blood
type would be roughly equal to the number of men with the same blood type?
If the statement is false, rewrite it so that it is true.

Question 28

Perform a chi-square homogeneity test, provided the conditions for the test are met. Use the P-value approach.
An independent simple random sample of 100 employees from 5 different companies was
selected, and the number who take public transportation to work was recorded. The results
are listed below, showing public transportation status and the five companies. At the 1%
significance level, test the claim that employees of the five companies are
nonhomogeneous with respect to public transportation status.

Question 29

Provide an appropriate response.

Question 30

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
A researcher performed a study to determine whether an association exists between sex
and blood type. He obtained the following sample data. At the 5% significance level, do the data provide sufficient evidence to conclude that an
association exists between sex and blood type?

Question 31

Solve the problem.
The table below shows a distribution and the observed frequencies of the values of a
variable from a simple random sample of a population. Perform a chi-square
goodness-of-fit test, at the specified significance level, to decide whether the distribution
of the variable differs from the given distribution.

Question 32

Perform the indicated goodness-of-fit test using the P-value method. Be sure to state the hypotheses and the significancelevel , to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
The U.S. Department of Defense provides data on the distribution of military personnel on
active duty by branch of service. Below is a table giving the percentage distribution for
1985. At the 5% significance level, do the data provide evidence that the current distribution of
military personnel on active duty differs from the 1985 distribution?

Question 33

Perform a chi-square homogeneity test, provided the conditions for the test are met. Use the critical-value approach.
300 men and 300 women were selected and asked whether they planned to vote in the
next election. The results of independent simple random samples are given in the table
below, showing the voting intentions by gender. Use a 1% significance level to test the
claim that there is a difference in the distribution of voting intentions for men and women.

Question 34

Provide an appropriate response.
Suppose that you have a contingency table showing political party affiliation cross
classified by age group for a certain population. Explain how you can determine whether
there is an association between age group and political party affiliation.

Question 35

Provide an appropriate response.
A researcher records for each of 500 randomly selected towns, the number of churches in
the town and the number of homicides in the town in the past ten years. The towns range
in size from a population of 1000 to a population of 1,000,000. He then performs a
chi-square test of independence for these two variables. Would you expect that he would
find association between the two variables? If so, should he conclude that a causal
relationship exists? Explain your thinking.

Question 36

Provide an appropriate response.
The contingency table below shows political party affiliation cross classified by age group
for a certain population. Obtain the conditional distribution of political party affiliation
within each age group and the marginal distribution of political party affiliation. Is there
association between the two variables? How can you tell?

Question 37

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
In studying the responses to a multiple-choice test question, the following sample data
were obtained. At the 0.05 significance level, test the claim that all five responses occur
with the same frequency.

Question 38

Perform the indicated goodness-of-fit test using the P-value method. Be sure to state the hypotheses and the significancelevel , to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
A study conducted for New Woman magazine indicates that the number of children
desired by newly-married American couples is distributed as follows. At the 1% significance level, does it appear that the "number of children desired"
distribution of California couples is different from that of the American population as a
whole?

Question 39

Provide an appropriate response.
Suppose that you wish to perform a chi-square test of independence. The sample data is
given in the contingency table below. Are the assumptions for the test met? If not, which
assumption is violated?

Question 40

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
In 1990, workplace accidents were distributed on workdays as follows. Do the data provide sufficient evidence to conclude that the distribution of workplace
accidents in 1995 differs from the 1990 distribution? Perform the hypothesis test at the 0.01
level of significance.

Question 41

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
Tests for adverse reactions to a new drug yielded the results given in the table. At the 0.05
significance level, do the data provide sufficient evidence to conclude that an association
exists between the treatment (drug or placebo)and the reaction (whether or not headaches
were experienced)?

Question 42

Provide an appropriate response.

Question 43

Provide an appropriate response.
The contingency table below shows political party affiliation cross classified by age group
for a certain population. What information would be given by the marginal distribution of
age group? How would you obtain this marginal distribution? What information would be
given by the marginal distribution of political party affiliation? How would you obtain this
marginal distribution?

Question 44

Provide an appropriate response.
Suppose that you wish to perform a chi-square test of independence. Give an example of
sample data for which assumption 1 (all expected frequencies are 1 or greater)is violated.
You should present the sample data in the form of a contingency table.

Question 45

-value.

Question 46

Use the contingency table to solve the problem.
The following contingency table shows the popular votes cast in the 1984 presidential election cross classified by region and political party. Data are in thousands, rounded to the nearest thousand. What percentage of the voters were in the Midwest?

A)40.6%
B)27.5%
C)11.3%
D)41.3%

Question 47

Provide an appropriate response.

Question 48

Provide an appropriate response.
What is the null hypothesis for the chi-square test of independence? What assumptions are
required for this test?

Question 49

Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of apercent if needed.
The contingency table below shows the income level for a random sample of adults cross classified by sex.

Question 50

Provide an appropriate response.
The table below shows the conditional distributions of the variable blood type for men and
for women for a certain population. Is there association between the two variables blood
type and sex? How can you tell?

Question 51

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
You roll a die 48 times with the following results. Do the data provide sufficient evidence to conclude that the die is loaded (i.e., that the six
numbers are not equally likely)? Perform the hypothesis test at the 0.05 level of
significance.

Question 52

Provide an appropriate response.

Question 53

-value.

Question 54

Provide an appropriate response.
When performing a chi-square goodness-of-fit test, why do large values of the test
statistic suggest that the variable does not have the distribution stated in the null
hypothesis? Refer to the formula for the test statistic in your explanation.

Question 55

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
A firm that manufactures engines for racing boats gathers data from all of its plants. The
table below gives the distribution of the life span of the engines (in numbers of months)for
the entire firm. At the 5% significance level, do the data provide evidence that the distribution of the life
spans of the engines manufactured at the Ohio plant is different from the firm's overall
distribution?

Question 56

Perform a chi-square independence test using the critical value approach, provided the conditions for using the test aremet. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
A researcher performed a study to determine whether an association exists between
political party affiliation and income. She obtained the following sample data. At the 10% significance level, do the data provide sufficient evidence to conclude that an
association exists between political party affiliation and income?

Question 57

Perform the indicated goodness-of-fit test. Be sure to state the hypotheses and the significance level, to obtain the criticalvalue, to compute the value of the test statistic, and to state your conclusion.
The U.S. Department of Defense provides data on the distribution of military personnel on
active duty by branch of service. Below is a table giving the percentage distribution for
1985. At the 5% significance level, do the data provide evidence that the current distribution of
military personnel on active duty differs from the 1985 distribution?

Question 58

Provide an appropriate response.
You have been using the chi-square test of independence to test for association between
two variables. Give an example of a pair of variables for which you would expect to find
no association. Give an example of a pair of variables for which you would expect to find
association, but not a causal relationship. Finally, give an example of a pair of variables for
which you would expect to find a causal relationship.

Question 59

Perform the indicated goodness-of-fit test using the P-value method. Be sure to state the hypotheses and the significancelevel , to compute the value of the test statistic, to obtain the P-value, and to state your conclusion.
A firm that manufactures engines for racing boats gathers data from all of its plants. The
table below gives the distribution of the life span of the engines (in numbers of months)for
the entire firm. At the 5% significance level, do the data provide evidence that the distribution of the life
spans of the engines manufactured at the Ohio plant is different from the firm's overall
distribution?

Question 60

Provide an appropriate response.
A chi-square goodness-of-fit test is to be performed. The relative frequencies for the null
hypothesis and the sample size are given. True or false, the assumptions for using a chi-square
goodness-of-fit test are satisfied?

Question 61

Question 62

Use the contingency table to solve the problem.
The following contingency table shows the popular votes cast in the 1984 presidential election cross classified by region and political party. Data are in thousands, rounded to the nearest thousand. What percentage of those who voted Republican were in the South?

A)58.8%
B)61.4%
C)32.5%
D)19.1%

Question 63

Use the contingency table to solve the problem.
The contingency table above shows the blood types of a sample of people cross classified by sex. What percentage of people in the sample have blood type B?

A)55.2%
B)29%
C)13%
D)7.2%

Question 64

Use the contingency table to solve the problem.
The contingency table above shows the blood types of a sample of patients cross classified by sex. How many of the men in the sample have blood type O?

A)48
B)42
C)90
D)110

Question 65

Provide an appropriate response.

Question 66

Use the contingency table to solve the problem.
The contingency table above shows the blood types of a sample of people cross classified by sex. What percentage of those people with blood type A are women?

A)47.6%
B)47.8%
C)44%
D)40.4%

Question 67

Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of apercent if needed.
During a poll, 129 people were randomly selected and asked their political party affiliation. The contingency table below shows the results cross classified by political party affiliation and sex.

Question 68

Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of apercent if needed.
Use the given contingency table to find the marginal distribution of the variable "income bracket".

Question 69

Provide an appropriate response.

Question 70

Use the contingency table to solve the problem.
The contingency table above shows the blood types of a sample of patients cross classified by sex. How many people in the sample have blood type B?

A)28
B)16
C)12
D)111

Question 71

Find the value of the chi-square test statistic for the goodness-of-fit test.
A firm that manufactures engines for racing boats gathers data from all of its plants. The table below gives the distribution of the life span of the engines (in number of months)for the entire
Firm.

Question 72

Find the value of the chi-square test statistic for the goodness-of-fit test.

Question 73

Use the contingency table to solve the problem.
The following contingency table shows the popular votes cast in the 1984 presidential election cross classified by region and political party. Data are in thousands, rounded to the nearest thousand. What percentage of the people voted Democrat and were in the West?

A)40.6%
B)39.2%
C)18.7%
D)7.6%

Question 74

Find the required value.