Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
78)
During a poll, 290 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.
42 48 53 143
48 59 40 147
18 20 12 50
108 127 105 340
Find the conditional distribution of the variable “income bracket” for Republicans.
78)
A)
Low: 31.8% ; Middle: 37.4% ; High: 30.9%
B)
Low: 44.4% ; Middle: 46.5% ; High: 38.1%
C)
Low: 29.4% ; Middle: 33.6% ; High: 37.1%
D)
Low: 32.7% ; Middle: 40.1% ; High: 27.2%
Provide an appropriate response.
79)
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: 0.35, 0.08, 0.12, 0.35, 0.1
79)
A)
True
B)
False
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
80)
During a poll, 147 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.
28 27 25 80
27 21 19 67
55 48 44 147
Find the marginal distribution of political party affiliation.
80)
A)
Democrats: 37.4% ; Republicans: 32.7% ; Other: 29.9%
B)
Democrats: 50.9% ; Republicans: 56.3% ; Other: 56.8%
C)
Democrats: 40.3% ; Republicans: 31.3% ; Other: 28.4%
D)
Men: 54.4% ; Women: 45.6%
Provide an appropriate response.
81)
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?
81)
A)
45% of this population are females with blood type O.
B)
45% of those with blood type O are female.
C)
45% of females have blood type O.
D)
45% of this population have blood type O.
82)
When conducting a chi–square homogeneity test, the P–value exceeds the specified significance
level. What can be concluded?
82)
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 required 2–value.
83)
For a 2–curve with 9 degrees of freedom, find 2
0.99 .
83)
A)
2.088
B)
1.646
C)
4.168
D)
21.666
Use the contingency table to solve the problem.
84)
45 51 6118
47 11 5110
92 27 11
The contingency table above shows the blood types of a sample of patients cross classified by sex.
Fill in the missing entries.
84)
A)
45 51 16 6118
47 47 11 5110
92 98 27 11 228
B)
45 51 71 6118
65 47 11 5110
92 98 27 11 228
43
C)
45 51 16 6118
47 47 11 5110
92 98 27 11 456
D)
45 51 38 6118
137 47 11 5110
92 98 27 11 228
85)
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?
85)
A)
19.1%
B)
61.4%
C)
32.5%
D)
58.8%
Find the required 2–value.
86)
For a 2–curve with 7 degrees of freedom, find the 2–value having area 0.05 to its right.
86)
A)
3.325
B)
2.167
C)
14.067
D)
15.507
Provide an appropriate response.
87)
True or false, a variable that has a 2–distribution can take only nonnegative values?
87)
A)
True
B)
False
Use the contingency table to solve the problem.
88)
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?
88)
A)
39.2%
B)
18.7%
C)
40.6%
D)
7.6%
89)
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”?
89)
A)
1.2%
B)
34.5%
Provide an appropriate response.
90)
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: 0.28, 0.16, 0.03, 0.51, 0.02
90)
A)
True
B)
False
91)
When conducting a chi–square homogeneity test, state the condition needed for the populations
under consideration to be homogeneous with respect to the variable.
91)
A)
The populations must both have normal distributions.
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 population proportions for the variable must not be not equal.
Use the contingency table to solve the problem.
92)
42 42 16 6106
43 51 14 5113
85 93 30 11 219
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?
92)
A)
7.3%
B)
30%
C)
53.3%
D)
13.7%
Find the required 2–value.
93)
For a 2–curve with 23 degrees of freedom, find 2
0.01 .
93)
A)
10.196
B)
40.289
C)
41.638
D)
32.007
Provide an appropriate response.
94)
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?
94)
A)
True
B)
False
Use the contingency table to solve the problem.
95)
The following contingency table provides a joint frequency distribution for a group of retired
people by career and age at retirement.
948 96 39 192
12 48 90 49 199
60 185 319 187 751
How many of the people were college professors who retired between 56 and 60?
95)
A)
199
B)
90
C)
185
D)
48
96)
42 55 11 4112
55 43 16 6120
97 98 27 10 232
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?
96)
A)
11
B)
112
C)
27
D)
16
Find the required 2–value.
97)
For a 2–curve with 18 degrees of freedom, find the 2–value having area 0.975 to its right.
97)
A)
7.564
B)
9.390
C)
8.231
D)
31.526
Use the contingency table to solve the problem.
98)
41 51 10 5107
41 44 12 3100
82 95 22 8207
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?
98)
A)
95
B)
107
C)
51
D)
100
Find the value of the chi–square test statistic for the goodness–of–fit test.
99)
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?
99)
A)
2= 52.176
B)
2= 427.196
C)
2= 107.937
D)
2= 462.711
Group the bivariate data into a contingency table.
100)
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
100)
50
M Other Middle
F Dem Low
M Dem Middle
M Rep Low
F Dem Middle
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.
101)
The contingency table below shows the income level for a random sample of adults cross classified
by sex.
30 23 10 63
23 28 960
53 51 19 123
Find the marginal distribution of the variable “income bracket”.
101)
A)
Low: 43.1% ; Middle: 41.5% ; High: 15.4%
B)
Low: 56.6% ; Middle: 45.1% ; High: 52.6%
C)
Male: 51.2% ; Female: 48.8%
D)
Low: 38.3% ; Middle: 46.7% ; High: 15%
Find the required 2–value.
102)
For a 2–curve with 27 degrees of freedom, find the 2–value having area 0.01 to its right.
102)
A)
36.741
B)
45.642
C)
12.879
D)
46.963
Use the contingency table to solve the problem.
103)
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?
103)
A)
177
B)
176
C)
44
D)
674
104)
40 48 10 7105
50 54 11 5120
90 102 21 12 225
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?
104)
A)
41.7%
B)
50%
C)
55.6%
D)
40%
Find the specified conditional or marginal distribution for the given contingency table. Round to the nearest tenth of a
percent if needed.
105)
During a poll, 138 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 26 26 70
26 30 12 68
44 56 38 138
Find the conditional distribution of political party affiliation for women.
105)
A)
Democrats: 59.5% ; Republicans: 53.6% ; Other: 31.6%
B)
Men: 50.7% ; Women: 49.3%
C)
Democrats: 38.2% ; Republicans: 44.1% ; Other: 17.6%
D)
Democrats: 31.9% ; Republicans: 40.6% ; Other: 27.5%
Provide an appropriate response.
106)
True or false, a 2–curve with 13 degrees of freedom resembles a normal curve more closely than a
2–curve with 3 degrees of freedom?
106)
A)
True
B)
False