Deck 27: Analysis of Variance

Question 1

A consumer interest group is interested in comparing the speed of four different desktop printers;four different documents are used for the experiment.Each test consists of randomly assigning one printer to one of the documents.The document is printed and the time to print in seconds is recorded.Each printer/document combination is tested.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 3;df-error = 15
B)df-treatment = 4;df-error = 15
C)df-treatment = 3;df-error = 13
D)df-treatment = 3;df-error = 12
E)df-treatment = 4;df-error = 12

Answer 1

df-treatment = 3;df-error = 12

Question 2

An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time.Five people are randomly assigned to each of the three assembly methods,and the total assembly time (in seconds)is recorded.

A)
B)
C)
D)
E)

Answer 2

Question 3

A mechanical engineer is studying bonding issues with the thermal protection tiles on the Space Shuttle.He wants to see whether there is any difference in the bonding strength between three different compounds.Fifteen tiles are randomly assigned to the three compounds so that each compound is tested on five tiles.Each tile is coated with its assigned compound and bonded to a surface.After a period of time,pull-tests are performed to determine the amount of force needed to break the bond.

A)
B)
C)
D)
E)

Answer 3

Question 4

An independent research firm conducts a study to compare the taste of four new sports drinks.Five people are randomly assigned to each of the four drinks.Each person tastes the drink and judges it on a scale from one to five.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 3;df-error = 19
B)df-treatment = 3;df-error = 17
C)df-treatment = 4;df-error = 17
D)df-treatment = 3;df-error = 16
E)df-treatment = 4;df-error = 16

Question 5

A consumer interest group is interested in comparing the speed of four different desktop printers;four different documents are used for the experiment.Each test consists of randomly assigning one printer to one of the documents.The document is printed and the time to print in seconds is recorded.Each printer/document combination is tested.

A)
B)
C)
D)
E)

Question 6

A mechanical engineer is studying bonding issues with the thermal protection tiles on the Space Shuttle.He wants to see whether there is any difference in the bonding strength between three different compounds.Fifteen tiles are randomly assigned to one of the three compounds so that each compound is tested on five tiles.Each tile is coated with its assigned compound and bonded to a surface.After a period of time,pull-tests are performed to determine the amount of force needed to break the bond.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 2;df-error = 12
B)df-treatment = 3;df-error = 12
C)df-treatment = 2;df-error = 14
D)df-treatment = 3;df-error = 14
E)df-treatment = 2;df-error = 13

Question 7

A hunting supply store is interested in knowing whether three different brands of goose decoys are equally effective in attracting geese.Each goose decoy is randomly assigned to five hunters,and the order of each experiment is also randomized.An experiment consists of a hunter using one goose decoy and waiting fifteen minutes.The number of geese attracted by the decoy is counted.

A)
B)
C)
D) equal
E) are equal

Question 8

A chemist is interested in comparing four different catalysts by measuring reaction times.Each catalyst is tested five times,with each experiment randomly assigned one of the four catalysts.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 4;df-error = 16
B)df-treatment = 3;df-error = 16
C)df-treatment = 4;df-error = 19
D)df-treatment = 3;df-error = 19
E)df-treatment = 3;df-error = 17

Question 9

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.

A) the alternative that all the wire type mean resistances are equal
B) the alternative that not all the wire size mean resistances are equal
C) the alternative that wire type and wire size mean resistances are equal
D) the alternative that all the wire size mean resistances are equal
E) the alternative that not all the wire type mean resistances are equal

Question 10

The Professional Golfer's Association (PGA)wants to know which brand of golf ball goes the farthest when hit by a driver.Three brands of golf balls are compared by using "Iron Byron" to randomly hit each brand of ball five times.The total distance in yards is measured after each ball comes to rest.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 2;df-error = 12
B)df-treatment = 2;df-error = 14
C)df-treatment = 3;df-error = 12
D)df-treatment = 3;df-error = 14
E)df-treatment = 2;df-error = 15

Question 11

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 4;df-error = 19
B)df-treatment = 3;df-error = 17
C)df-treatment = 3;df-error = 16
D)df-treatment = 4;df-error = 20
E)df-treatment = 3;df-error = 19

Question 12

The Professional Golfer's Association (PGA)wants to know which brand of golf ball goes the farthest when hit by a driver.Three brands of golf balls are compared by using "Iron Byron" to randomly hit each brand of ball five times.The total distance in yards is measured after each ball comes to rest.

A)
B)
C)
D)
E)

Question 13

An independent research firm conducts a study to compare the taste of four new sports drinks.Five people are randomly assigned to each of the four drinks.Each person tastes the drink and judges it on a scale from one to five.

A)
B)
C)
D)
E)

Question 14

A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.

A)
B)
C)
D)
E)

Question 15

A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed.Data from four past surveys are randomly chosen for each of the employees,and the percentage of completed questions is calculated.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 5;df-error = 19
B)df-treatment = 4;df-error = 19
C)df-treatment = 4;df-error = 15
D)df-treatment = 4;df-error = 16
E)df-treatment = 5;df-error = 15

Question 16

A chemist is interested in comparing four different catalysts by measuring reaction times.Each catalyst is tested five times,with each experiment randomly assigned one of the four catalysts.

A)
B)
C)
D)
E)

Question 17

A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 3;df-error = 21
B)df-treatment = 3;df-error = 20
C)df-treatment = 4;df-error = 20
D)df-treatment = 5;df-error = 21
E)df-treatment = 5;df-error = 20

Question 18

A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed.Data from four past surveys are randomly chosen for each of the employees,and the percentage of completed questions is calculated.

A) the alternative that not all survey mean percentages are equal
B) the alternative that all survey mean percentages are equal
C) the alternative that all employee mean percentages are equal
D) the alternative that employee and survey mean percentages are equal
E) the alternative that not all employee mean percentages are equal

Question 19

An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time.Five people are randomly assigned to each of the three assembly methods,and the total assembly time (in seconds)is recorded.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 2;df-error = 14
B)df-treatment = 3;df-error = 12
C)df-treatment = 2;df-error = 12
D)df-treatment = 2;df-error = 13
E)df-treatment = 3;df-error = 14

Question 20

A hunting supply store is interested in knowing whether three different brands of goose decoys are equally effective in attracting geese.Each goose decoy is randomly assigned to five hunters,and the order of each experiment is also randomized.An experiment consists of a hunter using one goose decoy and waiting fifteen minutes.How many degrees of freedom does the treatment sum of squares have? How about the error sum of squares?

A)df-treatment = 3;df-error = 14
B)df-treatment = 2;df-error = 13
C)df-treatment = 2;df-error = 14
D)df-treatment = 3;df-error = 12
E)df-treatment = 2;df-error = 12

Question 21

A chemist is interested in comparing four different catalysts by measuring reaction times.Each catalyst is tested five times,with each experiment randomly assigned one of the four catalysts.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 2.328;

=4.958;F-Ratio = 0.470;No,do not reject

Using α = 0.05.
B)

= 3.103;

=4.666;F-Ratio = 0.665;No,do not reject

Using α = 0.05.
C)

= 3.103;

=4.175;F-Ratio = 0.743;No,do not reject

Using α = 0.05.
D)

= 2.328;

=4.175;F-Ratio = 0.558;Yes,reject

Using α = 0.05.
E)

= 3.103;

=4.958;F-Ratio = 0.626;No,do not reject

Using α = 0.05.

Question 22

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 97.915;

=91.008;F-Ratio = 1.076;No,do not reject

Using α = 0.05.
B)

= 97.915;

=85.655;F-Ratio = 1.143;No,do not reject

Using α = 0.05.
C)

= 97.915;

=76.638;F-Ratio = 1.278;Yes,reject

Using α = 0.05.
D)

=73.436;

=76.638;F-Ratio = 0.958;No,do not reject

Using α = 0.05.
E)

=73.436;

=72.807;F-Ratio = 1.009;No,do not reject

Using α = 0.05.

Question 23

A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 56.793;

= 8.711;F-Ratio = 6.520;No,do not reject

Using α = 0.05.
B)

= 70.992;

= 8.711;F-Ratio = 8.150;Yes,reject

Using α = 0.05.
C)

= 56.793;

= 8.296;F-Ratio = 6.846;No,do not reject

Using α = 0.05.
D)

= 94.655;

= 8.711;F-Ratio = 10.866;Yes,reject

Using α = 0.05.
E)

= 94.655;

= 8.296;F-Ratio = 11.410;Yes,reject

Using α = 0.05.

Question 24

A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.The F-value from an ANOVA is 10.866.What is the P-value?

A)p = 0.0002
B)p = 0.010
C)p = 0.001
D)p = 0.0001
E)p = 0.0011

Question 25

A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.The box plots for the four types of fertilizer are shown below.

A)Yes,the widths of all the boxes are the same.
B)No,the data need to be log-transformed before conducting the ANOVA.
C)No,the centre lines for fertilizers three and four are higher than one and two.
D)Yes,the spreads of the four box plots appear similar enough to satisfy the assumption.
E)No,the data probably need to be re-expressed before conducting the ANOVA.

Question 26

A consumer interest group is interested in comparing the speed of four different desktop printers;four different documents are used for the experiment.Each test consists of randomly assigning one printer to one of the documents.The document is printed and the time to print in seconds is recorded.Each printer/document combination is tested.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 1.216;

=0.210;F-Ratio = 5.790;No,do not reject

Using α = 0.05.
B)

= 1.621;

=0.263;F-Ratio = 6.163;Yes,reject

Using α = 0.05.
C)

= 1.621;

=0.210;F-Ratio = 7.719;Yes,reject

Using α = 0.05.
D)

= 1.216;

=0.263;F-Ratio = 4.641;No,do not reject

Using α = 0.05.
E)

= 1.621;

=0.242;F-Ratio = 6.698;Yes,reject

Using α = 0.05.

Question 27

An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time.Five people are randomly assigned to each of the three assembly methods,and the total assembly time (in seconds)is recorded.The box plots for the three methods are shown below.

A)Yes,all the groups look like they are normally distributed.
B)Yes,the spreads look similar enough to proceed with the ANOVA.
C)No,the spreads of the three groups look different.The response may need to be re-expressed before proceeding with the ANOVA.
D)No,the centre line for method one is lower than the lines for methods two and three.
E)Yes,the widths of the boxes are all the same.

Question 28

A hunting supply store is interested in knowing whether three different brands of goose decoys are equally effective in attracting geese.Each goose decoy is randomly assigned to five hunters,and the order of each experiment is also randomized.An experiment consists of a hunter using one goose decoy and waiting fifteen minutes.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 4.467;

=0.486;F-Ratio = 9.191;Yes,reject

Using α = 0.05.
B)

= 4.467;

=0.523;F-Ratio = 8.541;Yes,reject

Using α = 0.05.
C)

= 2.978;

=0.567;F-Ratio = 5.252;No,do not reject

Using α = 0.05.
D)

= 4.467;

=0.567;F-Ratio = 7.878;Yes,reject

Using α = 0.05.
E)

= 2.978;

=0.486;F-Ratio = 6.128;No,do not reject

Using α = 0.05.

Question 29

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.The box plots for the four wire types are shown below.

A)Yes,the widths of the boxes are all the same.
B)Yes,all the groups look like they are normally distributed.
C)No,the spreads of the four groups look different.The response may need to be re-expressed before proceeding with the ANOVA.
D)No,the centre lines are steadily increasing.
E)Yes,the spreads look similar enough to proceed with the ANOVA.

Question 30

A mechanical engineer is studying bonding issues with the thermal protection tiles on the Space Shuttle.He wants to see whether there is any difference in the bonding strength between three different compounds.Fifteen tiles are randomly assigned to the three compounds so that each compound is tested on five tiles.Each tile is coated with its assigned compound and bonded to a surface.After a period of time,pull-tests are performed to determine the amount of force needed to break the bond.After collecting the data and analyzing the results,he reports that the F-ratio is 3.097.Assuming that the conditions required for ANOVA are satisfied,what is the P-value? What would you conclude?

A)p = 0.0827.Reject

Using α = 0.05.
B)p = 0.0827.Do not reject

Using α = 0.05.
C)p = 0.0827.Reject

Using α = 0.01.
D)p = 0.208.Do not reject

Using α = 0.05.
E)p = 0.0827.Do not reject

Using α = 0.10.

Question 31

A hunting supply store is interested in knowing whether three different brands of goose decoys are equally effective in attracting geese.Each goose decoy is randomly assigned to five hunters,and the order of each experiment is also randomized.An experiment consists of a hunter using one goose decoy and waiting fifteen minutes.The number of geese attracted by the decoy is counted.The data are analyzed and calculations show an F-ratio of 7.878.Assuming that the conditions required for ANOVA are satisfied,what is the P-value? What would you conclude?

A)p = 0.0065.Reject

Using α = 0.05.
B)p = 0.7001.Do not reject

Using α = 0.05.
C)p = 0.0703.Reject

Using α = 0.10.
D)p = 0.0065.Reject

Using α = 0.001.
E)p = 0.0703.Reject

Using α = 0.05.

Question 32

A mechanical engineer is studying bonding issues with the thermal protection tiles on the Space Shuttle.He wants to see whether there is any difference in the bonding strength between three different compounds.Fifteen tiles are randomly assigned to the three compounds so that each compound is tested on five tiles.Each tile is coated with its assigned compound and bonded to a surface.After a period of time,pull-tests are performed to determine the amount of force needed to break the bond.Calculate
,
,and the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 497.069;

= 206.346;F-Ratio =2.409;Yes,reject

Using α = 0.05.
B)

= 745.604;

= 206.346;F-Ratio = 3.613;Yes,reject

Using α = 0.05.
C)

= 497.069;

= 240.737;F-Ratio =2.065;No,do not reject

Using α = 0.05.
D)

= 745.604;

= 222.219;F-Ratio = 3.355;No,do not reject

Using α = 0.05.
E)

= 745.604;

= 240.737;F-Ratio = 3.097;No,do not reject

Using α = 0.05.

Question 33

An electrical engineer wants to compare the resistance of four types of wire made from different materials.Five wires of equal lengths and cross sectional areas are prepared for each of the four wire types.Each section of wire is randomly tested by sending a current through the wire and measuring the resistance.After collecting the data and analyzing the results,she reports that the F-ratio is 1.076.Assuming that the conditions required for ANOVA are satisfied,what is the P-value? What would you conclude?

A)p = 0.0871.Do not reject

Using α = 0.05.
B)p = 0.3872.Do not reject

Using α = 0.05.
C)p = 0.0871.Reject

Using α = 0.10.
D)p = 0.3872.Reject

Using α = 0.05.
E)p = 0.3872.Reject

Using α = 0.25.

Question 34

The Professional Golfer's Association (PGA)wants to know which brand of golf ball goes the farthest when hit by a driver.Three brands of golf balls are compared by using "Iron Byron" to randomly hit each brand of ball five times.The total distance in yards is measured after each ball comes to rest.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 468.458;

=122.296;F-Ratio =3.831;No,do not reject

Using α = 0.05.
B)

= 468.458;

=104.825;F-Ratio =4.469;No,do not reject

Using α = 0.05.
C)

= 702.688;

=97.837;F-Ratio = 7.182;Yes,reject

Using α = 0.05.
D)

= 702.688;

=104.825;F-Ratio = 6.703;Yes,reject

Using α = 0.05.
E)

= 702.688;

=122.296;F-Ratio = 5.746;Yes,reject

Using α = 0.05.

Question 35

A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed.Data from four past surveys are randomly chosen for each of the employees,and the percentage of completed questions is calculated.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 871.908;

=58.399;F-Ratio = 14.930;No,do not reject

Using α = 0.05.
B)

= 1089.885;

=54.749;F-Ratio = 19.907;Yes,reject

Using α = 0.05.
C)

= 1089.885;

=46.104;F-Ratio = 23.640;Yes,reject

Using α = 0.05.
D)

= 1089.885;

=58.399;F-Ratio = 18.663;Yes,reject

Using α = 0.05.
E)

= 871.908;

=46.104;F-Ratio = 18.912;No,do not reject

Using α = 0.05.

Question 36

An independent research firm conducts a study to compare the taste of four new sports drinks.Five people are randomly assigned to each of the four drinks.Each person tastes the drink and judges it on a scale from one to five.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 6.300;

=0.588;F-Ratio = 10.714;No,do not reject

Using α = 0.05.
B)

= 8.400;

=0.588;F-Ratio = 14.286;Yes,reject

Using α = 0.05.
C)

= 8.400;

=0.625;F-Ratio = 13.44;Yes,reject

Using α = 0.05.
D)

= 8.400;

=0.526;F-Ratio = 15.970;Yes,reject

Using α = 0.05.
E)

= 6.300;

=0.625;F-Ratio = 10.080;No,do not reject

Using α = 0.05.

Question 37

A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed.Data from four past surveys are randomly chosen for each of the employees,and the percentage of completed questions is calculated.The box plots for the five employees are shown below.

A)Yes,the widths of all the boxes are the same.
B)No,the data need to be log-transformed before conducting the ANOVA.
C)Yes,the spreads of the five box plots appear similar enough to satisfy the assumption.
D)No,the centre line for employee four is lower than all of the others
E)No,the data probably need to be re-expressed before conducting the ANOVA.

Question 38

An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time.Five people are randomly assigned to each of the three assembly methods,and the total assembly time (in seconds)is recorded.Calculate
,
And the F-ratio.Can you reject
Using α = 0.05? The ANOVA table is listed below.

A)

= 492767.954;

=19774.591;F-Ratio = 24.919;Yes,reject

Using α = 0.05.
B)

= 492767.954;

=23070.356;F-Ratio = 21.359;Yes,reject

Using α = 0.05.
C)

= 328511.969;

=23070.356;F-Ratio =14.240;Yes,reject

Using α = 0.05.
D)

= 328511.969;

=19774.591;F-Ratio =16.613;Yes,reject

Using α = 0.05.
E)

= 492767.954;

=21295.713;F-Ratio = 23.139;Yes,reject

Using α = 0.05.

Question 39

A consumer interest group is interested in comparing the speed of four different desktop printers;four different documents are used for the experiment.Each test consists of randomly assigning one printer to one of the documents.The document is printed and the time to print in seconds is recorded.Each printer/document combination is tested.The F-value from an ANOVA is 6.173.What is the P-value?

A)p = 0.0998
B)p = 0.0088
C)p = 0.0901
D)p = 0.9093
E)p = 0.0012