Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
Which of the following is not an assumption for performing a chi–square homogeneity test?
1)
A)
Samples are random.
B)
Samples are independent.
C)
All expected frequencies are 1 or greater.
D)
At most 20% of the expected frequencies are greater than 5.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Perform a chi–square homogeneity test, provided the conditions for the test are met. Use the critical–value approach.
2)
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.
Vaccinated Placebo Control
Caught the flu 819 21
Did not catch the flu 142 161 79
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.
2)
1
Provide an appropriate response.
3)
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?
3)
4)
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.
4)
5)
What assumptions are made when using a chi–square goodness–of–fit test?
5)
Perform the indicated goodness–of–fit test using the P–value method. Be sure to state the hypotheses and the significance
level , to compute the value of the test statistic, to obtain the P–value, and to state your conclusion.
6)
A die is rolled 180 times and the following data are obtained.
Number Frequency
1 31
2 34
3 26
4 16
5 32
6 41
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.
6)
Provide an appropriate response.
7)
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?
7)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
8)
The table below shows the age and favorite type of music of 668 randomly selected people.
Rock Jazz Classical
15–25 50 85 73
25–35 68 91 60
35–45 90 74 77
At the 0.05 significance level, do the data provide sufficient evidence to conclude that an
association exists between age and preferred music type?
8)
Provide an appropriate response.
9)
When performing a chi–square goodness–of–fit test, how are the expected frequencies
obtained?
9)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
10)
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?
Correct Incorrect
Math 27 53
English 43 37
10)
Provide an appropriate response.
11)
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.
11)
Perform the indicated goodness–of–fit test. Be sure to state the hypotheses and the significance level, to obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
12)
In 1990, workplace accidents were distributed on workdays as follows.
Day Mon Tues Wed Thur Fri
Percentage 25 15 15 15 30
In 1995, a random sample of 100 workplace accidents yielded the following data.
Day Mon Tues Wed Thur Fri
Percentage 30 13 13 14 30
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.
12)
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 the
test statistic, to obtain the P–value, and to state your conclusion.
13)
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?
13)
Perform the indicated goodness–of–fit test using the P–value method. Be sure to state the hypotheses and the significance
level , to compute the value of the test statistic, to obtain the P–value, and to state your conclusion.
14)
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.
Months Relative Frequency
Under 60 0.017
70–79 0.201
80–89 0.353
90–99 0.331
100–109 0.098
A random sample of 448 engines from the firm’s Ohio plant gives the following results.
Months Number of engines
Under 60 22
70–79 131
80–89 46
90–99 154
100–109 95
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?
14)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
15)
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?
Red Blue White
Car has been in accident 28 33 36
Car has not been in accident 23 22 30
15)
Provide an appropriate response.
16)
Explain the difference between univariate and bivariate data.
16)
17)
What is a chi–square goodness–of–fit test used for? For what kinds of variable can it be
used?
17)
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 the
test statistic, to obtain the P–value, and to state your conclusion.
18)
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?
18)
Perform a chi–square homogeneity test, provided the conditions for the test are met. Use the critical–value approach.
19)
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.
Win Loss
Suit 22 28
T–shirt 28 22
19)
Perform the indicated goodness–of–fit test. Be sure to state the hypotheses and the significance level, to obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
20)
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.
Branch of Service Percentage
Army 36.3
Navy 26.5
Marine Corps 9.2
Air Force 28.0
A random sample of 325 military personnel currently on active duty gave the following
statistics.
Branch of Service Frequency
Army 116
Navy 88
Marine Corps 36
Air Force 85
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?
20)
21)
You roll a die 48 times with the following results.
Number 1 2 3 4 5 6
Frequency 4 1 12 415 12
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.
21)
Provide an appropriate response.
22)
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.
22)
23)
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?
23)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
24)
A researcher performed a study to determine whether an association exists between sex
and blood type. He obtained the following sample data.
158 142
142 128
At the 5% significance level, do the data provide sufficient evidence to conclude that an
association exists between sex and blood type?
24)
Provide an appropriate response.
25)
Explain why a chi–square goodness–of–fit test is always right–tailed.
25)
26)
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?
26)
Perform a chi–square homogeneity test, provided the conditions for the test are met. Use the P–value approach.
27)
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.
Men Women
Plan to attend concert 230 255
Don’t plan to attend concert 170 145
27)
Perform a chi–square homogeneity test, provided the conditions for the test are met. Use the critical–value approach.
28)
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.
Men Women
Plan to vote 170 185
Do not plan to vote 130 115
28)
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 the
test statistic, to obtain the P–value, and to state your conclusion.
29)
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?
29)
Provide an appropriate response.
30)
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.
30)
31)
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.
31)
32)
In the chi–square test of independence, the test statistic used is 2=(O – E)2
E. Discuss the
meaning of O and E and explain the circumstances under which the 2values will be
smaller or larger. What is the relationship between a significant 2value and the values of
O and E?
32)
Perform the indicated goodness–of–fit test. Be sure to state the hypotheses and the significance level, to obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
33)
A study conducted for New Woman magazine indicates that the number of children
desired by newly–married American couples is distributed as follows.
Number of children desired Percent
0 9%
1 17%
2 55%
3 11%
Over 3 8%
A random sample of 600 couples in California resulted in the following data.
Number of children desired Frequency
069
1122
2334
357
Over 3 18
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?
33)
Provide an appropriate response.
34)
Suppose that you wish to perform a chi–square test of independence. True or false, if the
two variables are not associated, then the test statistic 2=(O – E)2
Ehas approximately a
chi–square distribution with rc – 1 degrees of freedom, where r and c are the number of
possible values for the two variables under consideration?
If the statement is false, explain why.
34)
35)
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?
35)
36)
Suppose that you wish to perform a chi–square test of independence. Give an example of
sample data for which assumption 2 (at most 20% of the expected frequencies are less than
5) is violated. You should present the sample data in the form of a contingency table.
36)
Perform the indicated goodness–of–fit test using the P–value method. Be sure to state the hypotheses and the significance
level , to compute the value of the test statistic, to obtain the P–value, and to state your conclusion.
37)
A study conducted for New Woman magazine indicates that the number of children
desired by newly–married American couples is distributed as follows.
Number of children desired Percent
0 9%
1 17%
2 55%
3 11%
Over 3 8%
A random sample of 600 couples in California resulted in the following data.
Number of children desired Frequency
0 55
1 118
2 340
3 60
Over 3 27
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?
37)
Solve the problem.
38)
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.
Distribution: 0.2 0.2 0.1 0.2 0.3
Observed frequencies: 37 15 12 23 43
Significance level = 0.05
38)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
39)
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”?
39)
19
40)
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?
40)
Perform a chi–square homogeneity test, provided the conditions for the test are met. Use the critical–value approach.
41)
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.
College A College B College C College D
Smoke 17 26 11 34
Don’t smoke 83 74 89 66
Use a 1% significance level to test the claim that the distribution of smoking status is
different at the four colleges.
41)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
42)
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?
42)
Provide an appropriate response.
43)
What is the null hypothesis for the chi–square test of independence? What assumptions are
required for this test?
43)
44)
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?
44)
Perform the indicated goodness–of–fit test using the P–value method. Be sure to state the hypotheses and the significance
level , to compute the value of the test statistic, to obtain the P–value, and to state your conclusion.
45)
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.
Branch of Service Percentage
Army 36.3
Navy 26.5
Marine Corps 9.2
Air Force 28.0
A random sample of 325 military personnel currently on active duty gave the following
statistics.
Branch of Service Frequency
Army 102
Navy 101
Marine Corps 40
Air Force 82
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?
45)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
46)
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)?
Drug Placebo
Headaches 11 7
No headaches 73 91
46)
Solve the problem.
47)
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.
Distribution: 0.25 0.15 0.15 0.15 0.3
Observed frequencies: 24 16 12 16 32
Significance level = 0.01
47)
Perform the indicated goodness–of–fit test. Be sure to state the hypotheses and the significance level, to obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
48)
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.
Months Relative Frequency
Under 60 0.017
70–79 0.201
80–89 0.353
90–99 0.331
100–109 0.098
A random sample of 448 engines from the firm’s Ohio plant gives the following results.
Months Number of engines
Under 60 22
70–79 131
80–89 46
90–99 154
100–109 95
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?
48)
Provide an appropriate response.
49)
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.
49)
Perform a chi–square homogeneity test, provided the conditions for the test are met. Use the P–value approach.
50)
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.
Companies
1 2 3 4 5
Use Public Trans. 18 25 12 33 22
Don’t Use Public Trans. 82 75 88 67 78
50)
Perform the indicated goodness–of–fit test. Be sure to state the hypotheses and the significance level, to obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
51)
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.
Response A B C D E
Frequency 12 15 16 18 19
51)
Perform a chi–square independence test using the critical 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 obtain the critical
value, to compute the value of the test statistic, and to state your conclusion.
52)
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?
52)
Solve the problem.
53)
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.
Distribution: 0.15 0.20 0.25 0.25 0.15
Observed frequencies: 12 15 16 18 19
Significance level = 0.10
53)
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 the
test statistic, to obtain the P–value, and to state your conclusion.
54)
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?
54)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Group the bivariate data into a contingency table.
27
55)
The table below provides theoretical data on marital status and income bracket for a random
sample of adults aged between 20 and 30. Group the bivariate data for the two variables into a
contingency table.
55)
A)
B)
C)
D)
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
56)
During a poll, 145 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.
23 27 30 80
22 23 20 65
45 50 50 145
Find the marginal distribution of political party affiliation.
56)
A)
Democrats: 33.8% ; Republicans: 35.4% ; Other: 30.8%
B)
Democrats: 51.1% ; Republicans: 54% ; Other: 60%
C)
Men: 55.2% ; Women: 44.8%
D)
Democrats: 31% ; Republicans: 34.5% ; Other: 34.5%
Provide an appropriate response.
57)
True or false, a 2–curve starts at 0 on the horizontal axis and extends indefinitely in both
directions approaching, but never touching, the horizontal axis as it does so?
57)
A)
True
B)
False
Use the contingency table to solve the problem.
58)
55 49 14 6124
54 54 12 7127
109 103 26 13 251
The contingency table above shows the blood types of a sample of patients cross classified by sex.
How many of the people in the sample are either women or have blood type AB?
58)
A)
124
B)
137
C)
6
D)
131
59)
The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
944 70 46 169
10 34 90 36 170
58 167 293 181 699
How many of the people who retired between 61 and 65 were attorneys?
59)
A)
90
B)
169
C)
293
D)
70
60)
The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
12 44 84 49 189
10 43 83 50 186
61 176 300 198 735
How many of the people retired later than age 55?
60)
A)
176
B)
44
C)
674
D)
177
Provide an appropriate response.
61)
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?
Sample size: n =50
Relative frequencies: 0.36 , 0.01, 0.23, 0.11, 0.29
61)
A)
True
B)
False
Find the required 2–value.
62)
For a 2–curve with 12 degrees of freedom, find 2
0.05.
62)
A)
19.675
B)
5.226
C)
23.336
D)
21.026
Provide an appropriate response.
63)
True or false, the total area under a 2–curve is equal to 1?
63)
A)
True
B)
False
Find the required 2–value.
64)
For a 2–curve with 18 degrees of freedom, find the 2–value having area 0.975 to its right.
64)
A)
7.564
B)
9.390
C)
31.526
D)
8.231
Group the bivariate data into a contingency table.
65)
The table below provides data on sex, political party affiliation, and income bracket for a sample of
people questioned during a poll. Group the bivariate data for the two variables “political party”
and “income bracket” into a contingency table.
Sex Political Party Income Bracket
M Rep High
F Dem Middle
F Dem Middle
M Dem Low
F Other Middle
M Rep Low
F Rep High
M Rep High
M Dem High
F Rep Low
M Dem High
F Rep Middle
F Dem Middle
M Dem Middle
M Rep Low
F Dem High
M Rep Low
F Other High
M Other Middle
65)
32
F Dem Low
M Dem Middle
M Rep Low
F Dem Middle
A)
B)
C)
D)
Use the contingency table to solve the problem.
66)
51 44 12 5112
51 44 15 7117
102 88 27 12 229
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?
66)
A)
44.4%
B)
27%
C)
5.2%
D)
11.8%
67)
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?
67)
A)
9.8%
B)
24.1%
C)
44.2%
D)
40.6%
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
68)
During a poll, 309 people were randomly selected and asked their political party affiliation. The
contingency table below shows the results cross classified by political party affiliation and income
bracket.
50 46 50 146
51 58 54 163
25 16 25 66
126 120 129 375
Find the conditional distribution of the variable “income bracket” for Republicans.
68)
A)
Low: 34.2% ; Middle: 31.5% ; High: 34.2%
B)
Low: 33.6% ; Middle: 32% ; High: 34.4%
C)
Low: 31.3% ; Middle: 35.6% ; High: 33.1%
D)
Low: 40.5% ; Middle: 48.3% ; High: 41.9%
Provide an appropriate response.
69)
The table below shows the conditional distributions of the variable blood type for men and for
women for a certain population. What information is given by the number in bold?
69)
A)
45% of females have blood type O.
B)
45% of this population have blood type O.
C)
45% of those with blood type O are female.
D)
45% of this population are females with blood type O.
Use the contingency table to solve the problem.
70)
The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
948 84 40 181
12 38 75 47 172
60 175 292 186 713
How many of the people were college professors who retired between 56 and 60?
70)
A)
38
B)
172
C)
75
D)
175
Group the bivariate data into a contingency table.
71)
The table below provides data on sex, political party affiliation, and income bracket for a sample of
people questioned during a poll. Group the bivariate data for the two variables “sex” and “political
party” into a contingency table.
Sex Political Party Income Bracket
M Rep High
F Dem Middle
F Dem Middle
M Dem Low
F Other Middle
M Rep Low
F Rep High
M Rep High
M Dem High
F Rep Low
M Dem High
F Rep Middle
F Dem Middle
M Dem Middle
M Rep Low
71)
36
F Dem High
M Rep Low
F Other High
M Other Middle
F Dem Low
M Dem Middle
M Rep Low
FDem Middle
A)
B)
C)
D)
Provide an appropriate response.
72)
When conducting a chi–square homogeneity test, the value of the test statistic exceeds the critical
value. What can be concluded?
72)
A)
Do not reject H0 at the given significance level.
B)
No conclusion can be made regarding H0 at the given significance level.
C)
Reject H0 at the given significance level.
Find the required 2–value.
73)
For a 2–curve with 3 degrees of freedom, find the 2–value having area 0.025 to its right.
73)
A)
7.378
B)
9.348
C)
0.216
D)
7.815
Provide an appropriate response.
74)
The table below shows the conditional distributions of the variable political party affiliation
corresponding to each age group for a certain population. What information is given by the
number 0.43?
74)
A)
43% of the population are Democrats.
B)
43% of those aged over 55 are Democrats.
C)
43% of the population are Democrats over the age of 55.
D)
43% of Democrats are over 55.
75)
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?
Sample size: n = 100
Relative frequencies: 0.29, 0.29, 0.03, 0.38, 0.01
75)
A)
True
B)
False
Use the contingency table to solve the problem.
76)
43 47 16 4110
44 51 16 4115
87 98 32 8225
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 do not have blood type O?
76)
A)
44
B)
71
C)
213
D)
115
77)
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?
77)
A)
58.8%
B)
61.4%
C)
32.5%
D)
19.1%
Group the bivariate data into a contingency table.
39
78)
The table below provides data on sex, political party affiliation, and income bracket for a sample of
people questioned during a poll. Group the bivariate data for the two variables “sex” and “income
bracket” into a contingency table.
Sex Political Party Income Bracket
M Rep High
F Dem Middle
F Dem Middle
M Dem Low
F Other Middle
M Rep Low
F Rep High
M Rep High
M Dem High
F Rep Low
M Dem High
F Rep Middle
F Dem Middle
M Dem Middle
M Rep Low
F Dem High
M Rep Low
F Other High
M Other Middle
F Dem Low
M Dem Middle
M Rep Low
F Dem Middle
78)
A)
B)
C)
D)
Find the value of the chi–square test statistic for the goodness–of–fit test.
79)
The following table is obtained from a random sample of 30 absences.
Day Mon Tue Wed Thur Fri
Number Absent 7 3 4 10 6
You wish to test the claim that the absences occur on the five days with equal frequency. What is the
value of the 2 test statistic? The observed frequencies and the expected frequencies are shown
below.
Observed
Frequency (O) Expected
Frequency (E)
7 6
3 6
4 6
10 6
6 6
79)
A)
2=3
B)
2=7.5
C)
2=5
D)
2=3.75
80)
You wish to test the claim that workplace accidents are distributed on workdays as follows:
Monday: 25%, Tuesday: 15%, Wednesday: 15%, Thursday: 15%, Friday: 30%. In a study of 100
workplace accidents, 28 occurred on a Monday, 13 occurred on a Tuesday, 14 occurred on a
Wednesday, 14 occurred on a Thursday, and 31 occurred on a Friday. What is the value of the 2
test statistic? The observed frequencies and the expected frequencies are shown below.
Observed
Frequency (O) Expected
Frequency (E)
28 25
13 15
14 15
14 15
31 30
80)
A)
2=0.793
B)
2=5.333
C)
2=2.286
D)
2=0.804
Find the required 2–value.
81)
For a 2–curve with 7 degrees of freedom, find the 2–value having area 0.05 to its right.
81)
A)
3.325
B)
14.067
C)
2.167
D)
15.507
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
82)
Use the given contingency table to find the conditional distribution of the
variable “marital status” for middle–income people.
82)
A)
Single: 43.8%; Married: 38.1%; Separated: 40%; Divorced: 37.5%
B)
Single: 35%; Married: 40%; Separated: 10%; Divorced: 15%
C)
Single: 25%; Married: 50%; Separated: 16.7%; Divorced: 8.3%
D)
Single: 32%; Married: 42%; Separated: 10%; Divorced: 16%
Provide an appropriate response.
83)
A chi–square homogeneity test is is to be conducted to decide whether five populations are
nonhomogeneous with respect to a variable that has seven possible values. What is the degrees of
freedom for the 2–statistic?
83)
A)
28
B)
24
C)
35
D)
30
Find the value of the chi–square test statistic for the goodness–of–fit test.
84)
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.
Months Relative frequency
Under 60 0.078
70 – 79 0.205
80 – 89 0.491
90 – 99 0.151
100 – 109 0.075
A random sample of 591 engines from the firm’s Ohio plant gives the following results.
Months Number of Engines
Under 60 105
70 – 79 26
80 – 89 152
90 – 99 182
100 – 109 126
You wish to test the claim that the distribution of the life spans of the engines manufactured at the
Ohio plant is the same as the firm’s overall distribution. What is the value of the 2 test statistic?
84)
A)
2= 427.196
B)
2= 107.937
C)
2= 52.176
D)
2= 462.711
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
85)
The contingency table below shows the income level for a random sample of adults cross classified
by sex.
26 28 963
25 26 758
51 54 16 121
Find the marginal distribution of the variable “income bracket”.
85)
A)
Male: 52.1% ; Female: 47.9%
B)
Low: 51% ; Middle: 51.9% ; High: 56.3%
C)
Low: 42.1% ; Middle: 44.6% ; High: 13.2%
D)
Low: 43.1% ; Middle: 44.8% ; High: 12.1%
Provide an appropriate response.
86)
The table below shows the conditional distributions of the variable political party affiliation
corresponding to each age group for a certain population. What percentage of Democrats are aged
between 35 and 55? If it is not possible to tell from the table, say so.
86)
A)
46%
B)
It is not possible to tell from this table.
C)
34%
D)
44.7%
Find the value of the chi–square test statistic for the goodness–of–fit test.
87)
According to recent research, the distribution of the number of children per family in the U.S. is as
follows.
Number of children Percent
More than 3 20.3
321.3
214.5
116.1
027.8
A random sample of 700 families with both parents under 40 yielded the following data.
Number of children Number of families
More than 3 154
3196
246
1101
0203
You wish to test the claim that the distribution of the number of children per family for families
with both parents under 40 is the same as that of the U.S. as a whole. What is the value of the 2 test
statistic? Note that the expected frequencies are as follows: more than 3 children: 142.1;
3 children: 149.1; 2 children: 101.5; one child: 112.7; 0 children: 194.6.
87)
A)
2= 13.781
B)
2= 80.807
C)
2= 32.091
D)
2= 47.674
Find the required 2–value.
88)
For a 2–curve with 10 degrees of freedom, find the 2–value having area 0.99 to its right.
88)
A)
23.209
B)
2.558
C)
24.725
D)
4.865
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
89)
Use the given contingency table to find the marginal distribution of the
variable “income bracket”.
89)
A)
Low: 24%; Middle: 40%; High: 36%
B)
Low: 40%; Middle: 40%; High: 20%
C)
Single: 32%; Married: 42%; Separated: 10%; Divorced: 16%
D)
Low: 18.8%; Middle: 43.8%; High: 37.5%
Provide an appropriate response.
90)
True or false, for a 2–curve with 18 degrees of freedom, 2
0.95 = – 2
0.05?
90)
A)
True
B)
False
91)
Suppose that a chi–square goodness–of–fit test is to be performed. True or false, the more closely
the observed frequencies match the expected frequencies, the larger the value of the test statistic 2
=(O – E)2
E?
91)
A)
True
B)
False
92)
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?
Sample size: n = 100
Relative frequencies: 0.31, 0.19, 0.12, 0.2, 0.18
92)
A)
True
B)
False
93)
When conducting a chi–square homogeneity test, the P–value exceeds the specified significance
level. What can be concluded?
93)
A)
Reject H0 at the given significance level.
B)
No conclusion can be made regarding H0 at the given significance level.
C)
Do not reject H0 at the given significance level.
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
94)
During a poll, 16 people were randomly selected and asked their political party affiliation. The
contingency table below shows the results cross classified by political party affiliation and income
bracket.
60 41 47 148
48 50 58 156
16 14 18 48
124 105 123 352
Find the marginal distribution of political party affiliation.
94)
A)
Democrats: 42% ; Republicans: 44.3% ; Other: 13.6%
B)
Low: 35.2% ; Middle: 29.8% ; High: 34.9%
C)
Democrats: 48.4% ; Republicans: 38.7% ; Other: 12.9%
D)
Democrats: 40.5% ; Republicans: 30.8% ; Other: 33.3%
Use the contingency table to solve the problem.
95)
54 47 13 3117
50 49 15 4118
104 96 28 7235
The contingency table above shows the blood types of a sample of people cross classified by sex.
What percentage of the men in the sample have blood type O?
95)
A)
50%
B)
44.3%
C)
48.1%
D)
42.4%
96)
52 42 15 7116
49 42 14 5110
101 84 29 12 226
The contingency table above shows the blood types of a sample of patients cross classified by sex.
How many men are in the sample?
96)
A)
101
B)
49
C)
110
D)
226
Provide an appropriate response.
97)
True or false, a 2–curve with 30 degrees of freedom resembles a normal curve more closely than a
2–curve with 6 degrees of freedom?
97)
A)
True
B)
False
Use the contingency table to solve the problem.
98)
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?
98)
A)
18.7%
B)
40.6%
C)
39.2%
D)
7.6%
Find the value of the chi–square test statistic for the goodness–of–fit test.
99)
You wish to test the claim that a die is fair. You roll it 48 times with the following results.
Number 1 2 3 4 5 6
Frequency 7 8 11 610 6
What is the value of the 2 test statistic? The observed frequencies and the expected frequencies are
shown below.
Observed
frequency (O) Expected
frequency (E)
7 8
8 8
11 8
6 8
10 8
6 8
99)
A)
2=3.667
B)
2=1.692
C)
2=2
D)
2=2.75
Use the contingency table to solve the problem.
100)
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?
100)
A)
27.5%
B)
11.3%
C)
40.6%
D)
41.3%
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
101)
The contingency table below shows the income level for a random sample of adults cross classified
by sex.
23 24 956
28 22 555
51 46 14 111
Find the conditional distribution of the variable “sex” for the middle–income people.
101)
A)
Male: 42.9% ; Female: 40%
B)
Male: 52.2% ; Female: 47.8%
C)
Male: 50.5% ; Female: 49.5%
D)
Low: 45.9% ; Middle: 41.4% ; High: 12.6%
Find the required 2–value.
102)
For a 2–curve with 23 degrees of freedom, find 2
0.01.
102)
A)
41.638
B)
10.196
C)
32.007
D)
40.289
D)
Use the contingency table to solve the problem.
103)
53 42 5115
50 13 3106
93 28 8
The contingency table above shows the blood types of a sample of patients cross classified by sex.
Fill in the missing entries.
103)
A)
53 42 75 5115
53 50 13 3106
93 92 28 8221
B)
53 42 15 5115
40 50 13 3106
93 92 28 8442
C)
53 42 15 5115
40 50 13 3106
93 92 28 8221
51
D)
53 42 41 5115
146 50 13 3106
93 92 28 8221
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
104)
The contingency table below shows the income level for a random sample of adults cross classified
by sex.
30 20 24 74
39 30 28 97
69 50 52 171
Find the conditional distribution of the variable “income bracket” for men.
104)
A)
Low: 40.5% ; Middle: 27% ; High: 32.4%
B)
Male: 43.3% ; Female: 56.7%
C)
Low: 43.5% ; Middle: 40% ; High: 46.2%
D)
Low: 40.4% ; Middle: 29.2% ; High: 30.4%
Use the contingency table to solve the problem.
105)
55 40 14 5114
47 55 13 5120
102 95 27 10 234
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?
105)
A)
114
B)
27
C)
14
D)
13
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
106)
During a poll, 105 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.
18 30 14 62
13 11 19 43
31 41 33 105
Find the conditional distribution of the variable “sex” for Democrats.
106)
A)
Male: 58.1% ; Female: 41.9%
B)
Democrats: 29.5% ; Republicans: 39% ; Other: 31.4%
C)
Male: 59% ; Female: 41%
D)
Male: 29% ; Female: 30.2%
Use the contingency table to solve the problem.
107)
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 in the West voted “Other”?
107)
A)
1.2%
B)
34.5%
Find the required 2–value.
108)
For a 2–curve with 9 degrees of freedom, find 2
0.99.
108)
A)
21.666
B)
4.168
C)
2.088
D)
1.646
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
109)
During a poll, 154 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.
23 29 26 78
26 28 22 76
49 57 48 154
Find the conditional distribution of political party affiliation for women.
109)
A)
Men: 50.6% ; Women: 49.4%
B)
Democrats: 34.2% ; Republicans: 36.8% ; Other: 28.9%
C)
Democrats: 31.8% ; Republicans: 37% ; Other: 31.2%
D)
Democrats: 63.6% ; Republicans: 49.1% ; Other: 45.8%
Find the required 2–value.
110)
For a 2–curve with 24 degrees of freedom, find 2
0.95.
110)
A)
12.401
B)
36.415
C)
13.091
D)
13.848
Provide an appropriate response.
111)
When conducting a chi–square homogeneity test, state the condition needed for the populations
under consideration to be homogeneous with respect to the variable.
111)
A)
The population proportions for the variable must not be not equal.
B)
The populations under consideration must have the same distribution for the variable.
C)
The populations under consideration must have different distributions for the variable.
D)
The populations must both have normal distributions.
Use the contingency table to solve the problem.
112)
48 51 15 5119
43 45 13 3104
91 96 28 8223
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?
112)
A)
48
B)
91
C)
43
D)
104
Provide an appropriate response.
113)
True or false, a 2–curve is symmetrical about 0?
113)
A)
True
B)
False
Use the contingency table to solve the problem.
114)
50 43 14 4111
55 46 12 4117
105 89 26 8228
The contingency table above shows the blood types of a sample of patients cross classified by sex.
How many of the people are women with blood type A?
114)
A)
117
B)
111
C)
43
D)
89
Provide an appropriate response.
115)
True or false, a variable that has a 2–distribution can take only nonnegative values?
115)
A)
True
B)
False
116)
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 the proportion of women in the sample with a given blood type would be
roughly equal to the proportion of men in the sample with the same blood type?
116)
A)
True
B)
False
Find the required 2–value.
117)
For a 2–curve with 27 degrees of freedom, find the 2–value having area 0.01 to its right.
117)
A)
45.642
B)
46.963
C)
36.741
D)
12.879
Use the contingency table to solve the problem.
118)
51 43 14 4112
54 54 13 7128
105 97 27 11 240
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?
118)
A)
38.4%
B)
43%
C)
46.7%
D)
44.3%
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