Deck 10: Chi-Square Tests and the F-Distribution

Question 1

A sociologist believes that the levels of educational attainment of homeless persons are not uniformly
distributed. To test this claim, you randomly survey 100 homeless persons and record the educational
attainment of each. The results are shown in the following table. Find the critical value χ to test the
sociologistʹs claim. Use = 0.10.

Answer 1

4.605

Question 2

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on
Until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting
Positions. Calculate the chi-square test statistic χ $$\chi ^ { 2 }$$ to test the claim that the number of wins is uniformly
Distributed across the different starting positions. The results are based on 240 wins. $$\begin{array} { c | c c c c c c } \text { Starting Position } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Number of Wins } & 45 & 36 & 33 & 50 & 32 & 44\end{array}$$

A)6.750
B)9.326
C)12.592
D)15.541

Answer 2

6.750

Question 3

The frequency distribution shows the ages for a sample of 100 employees. Find the expected frequencies for
each class to determine if the employee ages are normally distributed.

Answer 3

11, 26, 32, 21, and 7, respectively.

Question 4

A sociologist believes that the levels of educational attainment of homeless persons are not uniformly
distributed. To test this claim, you randomly survey 100 homeless persons and record the educational
attainment of each. The results are shown in the following table. At α = 0.10, is there evidence to support the
sociologistʹs claim that the distribution is not uniform?

Question 5

The frequency distribution shows the ages for a sample of 100 employees. Are the ages of employees normally
distributed? Use = 0.05.

Question 6

A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Calculate the chi-square test statistic χ $$\chi ^ { 2 }$$ to test the claim that the
Distribution is uniform.. $$\begin{array} { l | c l l l l } \text { Brand } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Customers } & 30 & 65 & 18 & 32 & 55\end{array}$$

A)37.45
B)45.91
C)48.91
D)55.63

Question 7

A sociologist believes that the levels of educational attainment of homeless persons are not uniformly
distributed. To test this claim, you randomly survey 100 homeless persons and record the educational
attainment of each. The results are shown in the following table. Calculate the chi-square test statistic χ to
test the sociologistʹs claim.

Question 8

Each side of a standard six-sided die should appear approximately $$\frac { 1 } { 6 }$$ of the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below.
Find the critical value χ $$x _ { 0 } ^ { 2 }$$ to test the playerʹs claim. Use $$\alpha = 0.10 .$$ $$\begin{array} { l | c c c c c c } \text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Frequency } & 11 & 15 & 12 & 16 & 17 & 19\end{array}$$

A)9.236
B)1.610
C)12.833
D)11.071

Question 9

Each side of a standard six-sided die should appear approximately $$\frac { 1 } { 6 }$$ oof the time when the die is rolled. A player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below.
Calculate the chi-square test statistic χ $$x ^ { 2 }$$ to test the playerʹs claim. $$\begin{array} { l | c c c c c c } \text { Number } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Frequency } & 15 & 12 & 16 & 19 & 17 & 11\end{array}$$

A)3.067
B)2.143
C)5.013
D)4.312

Question 10

Each side of a standard six-sided die should appear approximately of the time when the die is rolled. A
player suspects that a certain die is loaded. The suspected die is rolled 90 times. The results are shown below.
Test the playerʹs claim.

Question 11

Many track runners believe that they have a better chance of winning if they start in the inside lane that is
closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on
until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting
positions. Test the claim that the number of wins is uniformly distributed across the different starting
positions. The results are based on 240 wins.

Question 12

A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for
The 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic χ $$\chi ^ { 2 }$$ to test the claim that
All ages have crash rates proportional to their driving rates. $$\begin{array} { l | c c c c } \text { Age } & \text { Under 26 } & 26 - 45 & 46 - 65 & \text { Over 65 } \\\hline \text { Drivers } & 66 & 39 & 25 & 30\end{array}$$

A)75.101
B)85.123
C)101.324
D)95.431

Question 13

A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Find the
Critical value χ $$\chi _ { 0 } ^ { 2 }$$ to determine if the grade distribution for the department is different than expected. Use $$\alpha =$$ .01. $$\begin{array} { l | l l l l l } \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\\hline \text { Number } & 42 & 36 & 60 & 8 & 14\end{array}$$

A)13.277
B)11.143
C)9.488
D)7.779

Question 14

A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%;
F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Determine if
the grade distribution for the department is different than expected. Use

Question 15

Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on
Until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting
Positions. Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$ to test the claim that the number of wins is uniformly distributed across
The different starting positions. The results are based on 240 wins. $$\begin{array} { l | c c l l l l } \text { Starting Position } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Number of Wins } & 32 & 50 & 44 & 33 & 36 & 45\end{array}$$

A)11.070
B)9.236
C)15.086
D)12.833

Question 16

A teacher figures that final grades in the statistics department are distributed as: A, 25%; B, 25%; C, 40%; D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate
The chi-square test statistic χ $$x ^ { 2 }$$ to determine if the grade distribution for the department is different than
Expected. $$\begin{array} { l | l l l l l } \text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \\\hline \text { Number } & 36 & 42 & 60 & 8 & 14\end{array}$$

A)5.25
B)6.87
C)3.41
D)4.82

Question 17

A new coffeehouse wishes to see whether customers have any preference among 5 different brands of coffee. A
sample of 200 customers provided the data below. Test the claim that the distribution is uniform. Use = 0.01.

Question 18

A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$ to test the claim that the distribution is
Uniform. $$\text { Use } \alpha = 0.01 \text {. }$$ $$\begin{array} { l | c l l l l } \text { Brand } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Customers } & 30 & 32 & 55 & 65 & 18\end{array}$$

A)13.277
B)9.488
C)11.143
D)14.860

Question 19

A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age
distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for
the 46-65 group, and 12% for the group over 65. Test the claim that all ages have crash rates proportional to
their driving rates. Use = 0.05.

Question 20

A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for
The 45-65 group, and 12% for the group over 65. Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$ to test the claim that all ages have
Crash rates proportional to their driving rates. Use $$\alpha = 0.05$$ $$\begin{array} { l | c c c c } \text { Age } & \text { Under 26 } & 26 - 45 & 46 - 65 & \text { Over } 65 \\\hline \text { Drivers } & 66 & 39 & 25 & 30\end{array}$$

A)7.815
B)6.251
C)11.143
D)9.348

Question 21

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. $$\begin{array} { l | c c c } & { \text { Opinion } } \\\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \\\text { Republican } & 42 & 20 & 14 \\\text { Democrat } & 50 & 24 & 18 \\\text { Independent } & 10 & 16 & 6\end{array}$$ Find the chi-square test statistic, χ $$\chi ^ { 2 }$$ to test the claim of independence.

A)8.030
B)11.765
C)7.662
D)9.483

Question 22

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null
hypothesis and interpret the decision in the context of the original claim.
The data below shows the age and favorite type of music of 779 randomly selected people. Test the claim that preferred music type is dependent on age. Use

Question 23

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null
hypothesis and interpret the decision in the context of the original claim.
The contingency table below shows the party and opinions on a bill of a random sample of 200 state
representatives. Test the claim that opinions on the bill are dependent on party affiliation. Use α = 0.05 .

Question 24

A sports researcher is interested in determining if there is a relationship between the type of sport and type of team winning (home team versus visiting team). A random sample of 526 games is selected and the results are
Given below. Calculate the chi-square test statistic χ $$\chi ^ { 2 }$$
to test the claim that the type of team winning is
Independent of the sport. $$\begin{array} { l | c c c c } & \text { Football } & \text { Basketball } & \text { Soccer } & \text { Baseball } \\\hline \text { Home team wins } & 39 & 156 & 25 & 83 \\\text { Visiting team wins } & 31 & 98 & 19 & 75\end{array}$$

A)3.290
B)2.919
C)5.391
D)4.192

Question 25

A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Calculate the chi -square
Test statistic χ $$\chi ^ { 2 }$$ to determine if there is enough evidence to conclude that the number of minutes spent online
Per day is related to gender. $$\begin{array} { l | c c c c } & { \text { Minutes spent online per day } } \\\hline \text { Gender } & 0 - 30 & 30 - 60 & 60 - 90 & 90 + \\\text { Male } & 25 & 35 & 75 & 45 \\\text { Female } & 30 & 45 & 45 & 15\end{array}$$

A)18.146
B)19.874
C)20.912
D)21.231

Question 26

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null
hypothesis and interpret the decision in the context of the original claim.
A sports researcher is interested in determining if there is a relationship between the type of sport and type of
team winning (home team versus visiting team). A random sample of 526 games is selected and the results are
given below. Test the claim that the type of team winning is independent of the type of sport. Use

Question 27

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null
hypothesis and interpret the decision in the context of the original claim.
A researcher is interested in determining if there is a relationship between exercise and blood pressure for
adults over 50. A random sample of 236 adults over 50 is selected and the results are given below. Test the claim that walking and blood pressure are independent. Use

Question 28

A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given
Below. Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$ to test the claim that the number of home team and visiting team wins is
Independent of the sport. Use $$\alpha$$ = 0.01. $$\begin{array} { l | c c c c } & \text { Football } & \text { Basketball } & \text { Soccer } & \text { Baseball } \\\hline \text { Home team wins } & 39 & 156 & 25 & 83 \\\text { Visiting team wins } & 31 & 98 & 19 & 75\end{array}$$

A)11.345
B)12.838
C)7.815
D)9.348

Question 29

Find the indicated expected frequency.

-A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the expected
Frequency for the cell $$\mathrm { E } _ { 2,2 }$$ to determine if there is enough evidence to conclude that the number of minutes
Spent online per day is related to gender. Round to the nearest tenth if necessary. $$\begin{array} { l | c c c c } & { \text { Minutes spent online per day } } \\\hline \text { Gender } & 0 - 30 & 30 - 60 & 60 - 90 & 90 + \\\text { Male } & 23 & 35 & 76 & 46 \\\text { Female } & 31 & 42 & 46 & 16\end{array}$$

A)33
B)52.3
C)44
D)69.7

Question 30

Find the indicated expected frequency.

-A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given
Below. Find the expected frequency for $$\mathrm { E } _ { 2,2 }$$ tto test the claim that the number of home team and visiting team
Wins are independent of the sport. Round to the nearest tenth if necessary. $$\begin{array} { l | c c c c } & \text { Football } & \text { Basketball } & \text { Soccer } & \text { Baseball } \\\hline \text { Home team wins } & 41 & 154 & 27 & 81 \\\text { Visiting team wins } & 30 & 98 & 20 & 75\end{array}$$

A)106.8
B)19.9
C)145.2
D)27.1

Question 31

A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and
The results are given below. Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$
to test the claim that walking and low, moderate, and
High blood pressure are not related. Use $$\alpha$$ = 0.01. $$\begin{array} { l | c c c } \text { Blood Pressure } & \text { Low } & \text { Moderate } & \text { High } \\\hline \text { Walkers } & 35 & 62 & 25 \\\text { Non-walkers } & 21 & 65 & 28\end{array}$$

A)9.210
B)9.348
C)6.251
D)0.584

Question 32

A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the critical value $$\chi _ { 0 } ^ { 2 }$$ to determine if there is enough evidence to conclude that the number of minutes spent online per day is
Related to gender. Use $$\alpha$$ = 0.05. $$\begin{array} { l | c c c c } & { \text { Minutes spent online per day } } \\\hline \text { Gender } & 0 - 30 & 30 - 60 & 60 - 90 & 90 + \\\text { Male } & 25 & 35 & 75 & 45 \\\text { Female } & 30 & 45 & 45 & 15\end{array}$$

A)7.815
B)9.348
C)11.345
D)6.251

Question 33

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. $$\begin{array} { l | c c c } & { \text { Opinion } } \\\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \\\text { Republican } & 42 & 20 & 14 \\\text { Democrat } & 50 & 24 & 18 \\\text { Independent } & 10 & 16 & 6\end{array}$$ Find the critical value χ $$\chi _ { 0 } ^ { 2 }$$ , to test the claim of independence using α = 0.05.

A)9.488
B)7.779
C)11.143
D)13.277

Question 34

Find the marginal frequencies for the given contingency table

-The following contingency table was based on a random sample of drivers and classifies drivers by age group and number of accidents in the past three years. $$\begin{array} { c | c c c } \text { Number of }& {\quad\quad\quad \text { Age } } \\\text { accidents } & < 25 & 25 - 45 & > 45 \\\hline 0& 96 & 145 & 287 \\1& 20 & 67 & 62 \\> 1 & 20 & 8 & 26\end{array}$$

A) $\begin{array}{c|cccc}\text { Number of }& \text { Age }\\\text { accidents } & <25 & 25-45 & >45 & \text { Total } \\\hline 0 & 96 & 145 & 287 & 528 \\1 & 64 & 67 & 62 & 193 \\>1 & 20 & 8 & 26 & 54 \\\text { Total } & 180 & 220 & 375 & 775\end{array}$
B) $\begin{array}{c|cccc}\text { Number of } &\text { Age }\\ \text { accidents } & <25 & 25-45 & >45 & \text { Total } \\\hline 0 & 96 & 145 & 287 & 528 \\1 & 64 & 67 & 62 & 193 \\>1 & 20 & 8 & 26 & 54 \\\text { Total } & 180 & 220 & 385 & 785\end{array}$
C) $\begin{array}{c|cccc}\text { Number of } & \text { Age }\\\text { accidents } & <25 & 25-45 & >45 & \text { Total } \\\hline 0 & 96 & 145 & 287 & 528 \\1 & 64 & 67 & 62 & 225 \\>1 & 20 & 8 & 26 & 54 \\\text { Total } & 180 & 220 & 375 & 775\end{array}$
D) $\begin{array}{c|cccc}\text { Number of }& \text { Age }\\\text { accidents } & <25 & 25-45 & >45 & \text { Total } \\\hline 0 & 96 & 145 & 287 & 500 \\1 & 64 & 67 & 62 & 193 \\>1 & 20 & 8 & 26 & 54 \\\text { Total } & 180 & 215 & 375 & 770\end{array}$

Question 35

Find the marginal frequencies for the given contingency table

- $$\begin{array}{l}\quad\quad\quad\quad\quad\text { Blood Type }\\\begin{array} { l | c c c c } & O & \text { A } & \text { B } & \text { AB } \\\text { Sex } & & & & \\\hline \text { F } & 110 & 87 & 20 & 8 \\\text { M } & 71 & 74 & 16 & 4\end{array}\end{array}$$

A) $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Blood Type }$
$\begin{array}{|l|r|r|r|r|r|}\hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\\hline \text { F } & 110 & 87 & 20 & 8 & 225 \\\hline \text { M } & 71 & 74 & 16 & 4 & 165 \\\hline \text { Total } & 181 & 161 & 36 & 12 & 390\\\hline \end{array}$

B) $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Blood Type }$
$\begin{array}{|l|r|r|r|r|r|}\hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\\hline \text { F } & 110 & 87 & 20 & 8 & 225 \\\hline \text { M } & 71 & 74 & 16 & 4 & 160 \\\hline \text { Total } & 181 & 161 & 36 & 12 & 390\\\hline \end{array}$

C) $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Blood Type }$
$\begin{array}{|l|r|r|r|r|r|}\hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\\hline \text { F } & 110 & 87 & 20 & 8 & 235 \\\hline \text { M } & 71 & 74 & 16 & 4 & 165 \\\hline \text { Total } & 181 & 161 & 36 & 12 & 400\\\hline \end{array}$


D) $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Blood Type }$
$\begin{array}{|l|r|r|r|r|r|}\hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { A.B } & \text { Total } \\\hline \text { F } & 110 & 87 & 20 & 8 & 215 \\\hline \text { M } & 71 & 74 & 16 & 4 & 175 \\\hline \text { Total } & 181 & 161 & 36 & 17 & 390\\\hline \end{array}$

Question 36

Find the indicated expected frequency.

-The contingency table below shows the results of a random sample of 400 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. $$\begin{array} { l | c c c } &{ \quad\quad\quad\quad\quad\quad\text { Opinion } } \\\hline \text { Party } & \text { Approve } & \text { Disapprove } & \text { No Opinion } \\\text { Republican } & 84 & 40 & 28 \\\text { Democrat } & 100 & 48 & 36 \\\text { Independent } & 20 & 32 & 12\end{array}$$ Find the expected frequency for the cell $$\mathrm { E } _ { 2,2 } \text {. }$$ Round to the nearest tenth if necessary.

A)55.2
B)45.6
C)93.84
D)34.96

Question 37

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value. Calculate the test statistic. Decide to reject or to fail to reject the null
hypothesis and interpret the decision in the context of the original claim.
A researcher wants to determine whether the time spent online per day is related to gender. A random sample
of 315 adults was selected and the results are shown below. Test the hypothesis that the time spent online per day is related to gender. Use

Question 38

Find the marginal frequencies for the given contingency table

-The table below describes the smoking habits of a group of asthma sufferers. $$\begin{array} { l | c c c } & \text { Nonsmoker } & \text { Light smoker } & \text { Heavy smoker } \\\hline \text { Men } & 393 & 90 & 77 \\\text { Women } & 355 & 80 & 76\end{array}$$

A) $$\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\& \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\\hline \text { Men } & 393 & 90 & 77 & 560 \\\text { Women } & 355 & 80 & 76 & 511 \\\text { Total } & 748 & 170 & 153 & 1071\end{array}$$
B) $$\begin{array} { r | c c c r } &\text { Non- } & \text { Light } & \text { Heavy } \\&\text { smoker }& \text { smoker } & \text { smoker } & \text { Total } \\\hline \text { Men } & 393 & 90 & 77 & 560 \\\text { Women } & 355 & 80 & 76 & 511 \\\text { Total } & 748 & 170 & 118 & 1071\end{array}$$
C) $$\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\& \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\\hline \text { Men } & 393 & 90 & 77 & 560 \\\text { Women } & 355 & 80 & 76 & 583 \\\text { Total } & 748 & 170 & 153 & 1071\end{array}$$
D) $$\begin{array} { r | c c c r } & \text { Non- } & \text { Light } & { \text { Heavy } } \\& \text { smoker } & \text { smoker } & \text { smoker } & \text { Total } \\\hline \text { Men } & 393 & 90 & 77 & 415 \\\text { Women } & 355 & 80 & 76 & 511 \\\text { Total } & 748 & 182 & 153 & 1071\end{array}$$

Question 39

Find the indicated expected frequency.

-A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and
The results are given below. Find the expected frequency $$\mathrm { E } _ { 2,2 }$$ to test the claim that walking and low, moderate,
And high blood pressure are not related. Round to the nearest tenth if necessary. $$\begin{array} { l | c c c } \text { Blood Pressure } & \text { Low } & \text { Moderate } & \text { High } \\\hline \text { Walkers } & 38 & 64 & 20 \\\text { Non-walkers } & 24 & 63 & 27\end{array}$$

A)61.3
B)29.9
C)65.7
D)22.7

Question 40

A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and
The results are given below. Calculate the chi-square test statistic χ $$\chi ^ { 2 }$$
to test the claim that walking and low,
Moderate, and high blood pressure are not related. $$\begin{array} { l | c c c } \text { Blood Pressure } & \text { Low } & \text { Moderate } & \text { High } \\\hline \text { Walkers } & 35 & 62 & 25 \\\text { Non-walkers } & 21 & 65 & 28\end{array}$$

A)3.473
B)16.183
C)18.112
D)6.003

Question 41

Perform a homogeneity of proportions test to test whether the population proportions are equal. The hypotheses to be
tested are:
H₀: The proportions are equal
H_a: At least one of the proportions is different from the others.
Random samples of 400 men and 400 women were obtained and participants were asked whether they
planned to vote in the next election. The results are listed below. Perform a homogeneity of proportions test to
test the claim that the proportion of men who plan to vote in the next election is the same as the proportion of
women who plan to vote. Use = 0.05.

Question 42

Calculate the test statistic F to test the claim that $$\sigma _ { 1 } ^ { 2 } = \sigma _{ 2 }^ { 2 } .$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 13 & \mathrm { n } _ { 2 } = 12 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 17.248 & \mathrm {~s} _ { 2 } ^ { 2 } = 13.75\end{array}$$

A)1.254
B)0.797
C)1.120
D)1.573

Question 43

Calculate the test statistic F to test the claim that $$\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 25 & \mathrm { n } _ { 2 } = 30 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 6.498 & \mathrm {~s} _ { 2 } ^ { 2 } = 4.05\end{array}$$

A)1.604
B)1.267
C)0.623
D)2.573

Question 44

Find the critical value $$\mathrm { F } _ { 0 }$$ to test the claim that $$\sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^{ 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use α $$\alpha = 0.05 \text {. }$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 15 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 8.41 & \mathrm {~s} _ { 2 } ^ { 2 } = 7.84\end{array}$$

A)2.46
B)3.66
C)2.95
D)2.40

Question 45

Find the critical value $$\mathrm { F } _ { 0 }$$ to test the claim that $$\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.02$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 13 & \mathrm { n } _ { 2 } = 12 \\\\\mathrm {~s} \frac { 2 } { 1 } = 7.84 & \mathrm {~s} _ { 2 } ^ { 2 } = 6.25\end{array}$$

A)4.40
B)2.79
C)4.25
D)3.43

Question 46

Calculate the test statistic F to test the claim that $$\sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 15 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 12.615 & \mathrm {~s} _ { 2 } ^ { 2 } = 11.76\end{array}$$

A)1.073
B)0.932
C)1.036
D)1.151

Question 47

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
Test the claim that Two samples are randomly selected from populations that are normal. The
sample statistics are given below. Use

Question 48

Find the critical value $$\mathrm { F } _ { 0 }$$ for a one-tailed test using α $$\alpha$$ = 0.05, d.f.N = 6, and d.f.D = 16.

A)2.74
B)3.94
C)2.66
D)2.19

Question 49

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
Test the claim that Two samples are randomly selected from populations that are normal. The
sample statistics are given below. Use

Question 50

Calculate the test statistic F to test the claim that $$\sigma _ { 1 } ^ { 2 } > \sigma { } _ { 2 } ^ { 2 } .$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 13 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 4800 & \mathrm {~s} _ { 2 } ^ { 2 } = 1875\end{array}$$

A)2.560
B)1.600
C)0.391
D)6.554

Question 51

Find the critical value $$\mathrm { F } _ { 0 }$$ for a two-tailed test using α $$\alpha$$ = 0.05, d.f.N = 5, and d.f.D = 10.

A)4.24
B)4.07
C)4.47
D)6.62

Question 52

Perform a homogeneity of proportions test to test whether the population proportions are equal. The hypotheses to be
tested are:
H₀: The proportions are equal
H_a: At least one of the proportions is different from the others.
A random sample of 100 students from 5 different colleges was randomly selected, and the number who smoke
was recorded. The results are listed below. Perform a homogeneity of proportions test to test the claim that the
proportion of students who smoke is the same in all 5 colleges. Use

Question 53

Find the critical value $$\mathrm { F } _ { 0 }$$ to test the claim that $$\sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 } \text {. }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.05$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 25 & \mathrm { n } _ { 2 } = 30 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 3.61 & \mathrm {~s} _ { 2 } ^ { 2 } = 2.25\end{array}$$

A)2.15
B)2.21
C)2.14
D)2.09

Question 54

Find the critical value $$\mathrm { F } _ { 0 }$$ for a two-tailed test using α $$\alpha$$ = 0.02, d.f.N = 5, and d.f.D = 10.

A)5.64
B)10.05
C)5.99
D)5.39

Question 55

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
Test the claim that Two samples are randomly selected from populations that are normal. The
sample statistics are given below. Use

Question 56

Calculate the test statistic F to test the claim that $$\sigma _ { 1 } ^ { 2 } \geq \sigma _ { 2 } ^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 13 & \mathrm { n } _ { 2 } = 12 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 35.224 & \mathrm {~s} _ { 2 } ^ { 2 } = 28.083\end{array}$$

A)1.254
B)0.797
C)1.573
D)1.120

Question 57

Find the critical value $$\mathrm { F } _ { 0 }$$ for a one-tailed test using α $$\alpha$$ = 0.01, d.f.N = 3, and d.f.D = 20.

A)4.94
B)25.58
C)5.82
D)3.09

Question 58

Find the critical value $$F _ { 0 }$$ to test the claim that $$\sigma _ { 1 } ^ { 2 } > \sigma _{ 2 }^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.01 .$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 13 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 1600 & \mathrm {~s} _ { 2 } ^ { 2 } = 625\end{array}$$

A)4.01
B)3.18
C)2.62
D)3.67

Question 59

Find the critical value $$\mathrm { F } _ { 0 }$$ to test the claim that $$\sigma \underset { 1 } { 2 } \neq \sigma _{ 2 }^{ 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.02$$ $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 0.578 & \mathrm {~s} _ { 2 } ^ { 2 } = 0.260\end{array}$$

A)3.59
B)2.45
C)2.92
D)4.56

Question 60

Calculate the test statistic F to test the claim that $$\begin{array} { r } \sigma_ { 1 }^ { 2 }\\\end{array} \neq \sigma_ { 2 }^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l } \mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\\\\mathrm {~s} _ { 1 } ^ { 2 } = 1.156 & \mathrm {~s} _ { 2 } ^ { 2 } = 0.52\end{array}$$

A)2.223
B)1.490
C)4.933
D)0.450

Question 61

The weights of a random sample of 25 women between the ages of 25 and 34 had a standard deviation of 28
pounds. The weights of a random sample of 41 women between the ages of 55 and 64 had a standard
deviation of 21 pounds. Construct a 95% confidence interval for are the variances of
the weights of women between the ages 25 and 34 and the weights of women between the ages of 55 and 64
respectively.

Question 62

Find the left-tailed and right-tailed critical F-values for a two-tailed test. Let α = 0.02, d.f.N = 7, and
d.f.D = 5.

Question 63

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
Test the claim that Two samples are randomly selected from populations that are normal. The
sample statistics are given below. Use

Question 64

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
The weights of a random sample of 121 women between the ages of 25 and 34 had a standard deviation of 28
pounds. The weights of 121 women between the ages of 55 and 64 had a standard deviation 21 pounds. Test
the claim that the older women are from a population with a standard deviation less than that for women in
the 25 to 34 age group. Use

Question 65

Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Find the critical value F0 to test the claim that the type of fertilizer makes no
Difference in the mean number of raspberries per plant. Use $$\alpha = 0.01$$ $$\begin{array} { c c c c } \hline \text { Fertilizer 1 } & \text { Fertilizer 2 } & \text { Fertilizer 3 } & \text { Fertilizer 4 } \\\hline 6 & 8 & 6 & 3 \\5 & 5 & 3 & 5 \\6 & 5 & 3 & 3 \\7 & 5 & 4 & 4 \\7 & 5 & 2 & 4 \\6 & 6 & 3 & 5\end{array}$$

A)4.94
B)4.43
C)26.69
D)4.22

Question 66

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
A statistics teacher wants to see whether there is a significant difference between the variance of the ages of day
students and the variance of the ages of night students. A random sample of 31 students is selected from each
group. The data are given below. Test the claim that there is no difference between the variances of the two
groups.
Use

Question 67

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
At a college, 61 female students were randomly selected and it was found that their monthly income had a
standard deviation of $218.70. For 121 male students, the standard deviation was $303.66. Test the claim that
variance of monthly incomes is higher for male students than it is for female students. Use

Question 68

A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given
Medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six
Weeks, each subjectʹs blood pressure is recorded. Find the critical value $$\mathrm { F } _ { 0 }$$ to test the claim that there is no
Difference among the means. Use $$\alpha$$ = 0.05. $$\begin{array} { c c c } \hline \text { Group 1 } & \text { Group 2 } & \text { Group 3 } \\\hline 9 & 8 & 4 \\12 & 2 & 12 \\11 & 3 & 4 \\15 & 5 & 8 \\13 & 4 & 9 \\8 & 0 & 6\\\hline\end{array}$$

A)3.68
B)19.43
C)4.77
D)39.43

Question 69

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
A statistics teacher believes that the variance of test scores of students in her evening statistics class is lower
than the variance of test scores of students in her day class. The results of an exam, given to the day and
evening students, are shown below. Can the teacher conclude that the scores of evening students have a lower
variance? Use

Question 70

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
Test the claim that Two samples are randomly selected from populations that are normal. The
sample statistics are given below. Use

Question 71

Find the test statistic F to test the claim that the populations have the same mean. $$\begin{array} { l c c } \hline \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } \\\hline \mathrm { n } = 8 & \mathrm { n } = 8 & \mathrm { n } = 8 \\\overline { \mathrm { x } } = 3.0 & \overline { \mathrm { x } } = 2.6 & \overline { \mathrm { x } } = 2.6 \\\mathrm {~s} = 0.50 & \mathrm {~s} = 0.60 & \mathrm {~s} = 0.55 \\\hline\end{array}$$

A)1.403
B)1.021
C)1.182
D)0.832

Question 72

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
A random sample of 21 women had blood pressure levels with a variance of 553.6. A random sample of 18 men
had blood pressure levels with a variance of 368.64. Test the claim that the blood pressure levels for women
have a larger variance than those for men. Use

Question 73

Find the left-tailed and right-tailed critical F-values for a two-tailed test. Use the sample statistics below. Let α = 0.05.

Question 74

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
A local bank has the reputation of having a variance in waiting times as low as that of any bank in the area. A
competitor bank in the area checks the waiting time at both banks and claims that its variance of waiting times
is lower than at the local bank. The sample statistics are listed below. Test the competitorʹs claim. Use

Question 75

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
A medical researcher suspects that the variance of the pulse rate of smokers is higher than the variance of the
pulse rate of non-smokers. Use the sample statistics below to test the researcherʹs suspicion. Use α = 0.05.

Question 76

Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Find the test statistic F to test the claim that the type of fertilizer makes no
Difference in the mean number of raspberries per plant.
$$\begin{array} { c c c c } \hline \text { Fertilizer 1 } & \text { Fertilizer 2 } & \text { Fertilizer 3 } & \text { Fertilizer 4 } \\\hline 6 & 8 & 6 & 3 \\7 & 5 & 3 & 5 \\6 & 5 & 2 & 3 \\5 & 5 & 4 & 4 \\7 & 5 & 3 & 5 \\6 & 6 & 3 & 4 \\\hline\end{array}$$

A)8.357
B)8.123
C)7.123
D)6.912

Question 77

A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given
Medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six
Weeks, each subjectʹs blood pressure is recorded. Find the test statistic F to test the claim that there is no
Difference among the means. $$\begin{array} { c c c } \hline \text { Group 1 } & \text { Group 2 } & \text { Group 3 } \\\hline 13 & 8 & 6 \\12 & 5 & 12 \\11 & 3 & 4 \\15 & 2 & 8 \\9 & 4 & 9 \\8 & 0 & 4\end{array}$$ 949
804

A)11.095
B)9.812
C)8.369
D)12.162

Question 78

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
A study was conducted to determine if the variances of elementary school teacher salaries from two
neighboring districts were equal. A sample of 25 teachers from each district was selected. The first district had
a standard deviation of = $4830, and the second district had a standard deviation = $4410. Test the claim
that the variances of the salaries from both districts are equal. Use

Question 79

Find the critical $$\mathrm { F } _ { 0 }$$ -value to test the claim that the populations have the same mean. Use $$\alpha = 0.05 \text {. }$$ $$\begin{array} { l c l } \hline \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } \\\hline \mathrm { n } = 8 & \mathrm { n } = 8 & \mathrm { n } = 8 \\\overline { \mathrm { x } } = 3.0 & \overline { \mathrm { x } } = 2.6 & \overline { \mathrm { x } } = 2.6 \\\mathrm {~s} = 0.50 & \mathrm {~s} = 0.60 & \mathrm {~s} = 0.55 \\\hline\end{array}$$

A)3.47
B)3.210
C)2.819
D)1.892

Question 80

Perform the indicated hypothesis test. Be sure to do the following: identify the claim and state the null and alternative
hypotheses. Determine the critical value and rejection region. Calculate the test statistic. Decide to reject or to fail to
reject the null hypothesis and interpret the decision in the context of the original claim. Assume that the samples are
independent and that each population has a normal distribution.
A local bank has the reputation of having a variance in waiting times as low as that of any bank in the area. A
competitor bank in the area checks the waiting time at both banks and claims that its variance of waiting times
is lower than at the local bank. The sample statistics are listed below. Test the competitorʹs claim. Use