Deck 11: Analysis of Variance

Question 1

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the mean, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is given below. How should the data be analyzed?

A) F test for differences in variances.
B) one-way ANOVA F test.
C) t test for the differences in means.
D) t test for the mean difference.

Answer 1

one-way ANOVA F test.

Question 2

A completely randomized design

A) has only one factor with several treatment groups.
B) can have more than one factor, each with several treatment groups.
C) has one factor and one block.
D) has one factor and one block and multiple values.

Answer 2

has only one factor with several treatment groups.

Question 3

TABLE 11-2
An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

Referring to Table 11-2, the within groups degrees of freedom is

A) 3
B) 4
C) 16
D) 19

Answer 3

16

Question 4

In a two-way ANOVA the degrees of freedom for the "error" term is

A) (r - 1)(c - 1).
B) rc(n' - 1).
C) (r - 1).
D) rcn' + 1.

Question 5

The F test statistic in a one-way ANOVA is

A) MSW/MSA.
B) SSW/SSA.
C) MSA/MSW.
D) SSA/SSW.

Question 6

In a one-way ANOVA, if the computed F statistic exceeds the critical F value we may

A) reject H₀ since there is evidence all the means differ.
B) reject H₀ since there is evidence of a treatment effect.
C) not reject H₀ since there is no evidence of a difference.
D) not reject H₀ because a mistake has been made.

Question 7

Which of the following components in an ANOVA table are not additive?

A) sum of squares
B) degrees of freedom
C) mean squares
D) It is not possible to tell.

Question 8

TABLE 11-1
Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at Duke University participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. Unknown to the subject, the test taker was a bogus student who was working with the researchers. The experimenters manipulated two factors: subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of the test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data were subjected to appropriate analyses with the following results.

Referring to Table 11-1, at the 0.01 level, what conclusions can you reach from the analysis?

A) At the 0.01 level, subject visibility and test taker success are significant predictors of latency feedback.
B) At the 0.01 level, the model is not useful for predicting latency to feedback.
C) At the 0.01 level, there is evidence to indicate that subject visibility and test taker success interact.
D) At the 0.01 level, there is no evidence of interaction between subject visibility and test taker success.

Question 9

TABLE 11-1
Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at Duke University participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. Unknown to the subject, the test taker was a bogus student who was working with the researchers. The experimenters manipulated two factors: subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of the test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data were subjected to appropriate analyses with the following results.

Referring to Table 11-1, what type of experimental design was employed in this study?

A) completely randomized design with 4 treatments
B) randomized block design with four treatments and 10 blocks
C) 2 x 2 factorial design with 10 replications
D) None of the above.

Question 10

TABLE 11-2
An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

Referring to Table 11-2, at a significance level of 1%,

A) there is insufficient evidence to conclude that the mean number of customers bumped by the 4 packages are not all the same.
B) there is insufficient evidence to conclude that the mean number of customers bumped by the 4 packages are all the same.
C) there is sufficient evidence to conclude that the mean number of customers bumped by the 4 packages are not all the same.
D) there is sufficient evidence to conclude that the mean number of customers bumped by the 4 packages are all the same.

Question 11

In a two-way ANOVA the degrees of freedom for the interaction term is

A) (r - 1)(c - 1).
B) rc(n - 1).
C) (r - 1).
D) rcn + 1.

Question 12

The degrees of freedom for the F test in a one-way ANOVA are

A) (n - c) and (c - 1).
B) (c - 1) and (n - c).
C) (c - n) and (n - 1).
D) (n - 1) and (c - n).

Question 13

In a one-way ANOVA

A) an interaction term is present.
B) an interaction effect can be tested.
C) there is no interaction term.
D) the interaction term has (c - 1)(n - 1) degrees of freedom.

Question 14

TABLE 11-2
An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

Referring to Table 11-2, the among-group (between-group) mean squares is

A) 8.525
B) 70.8
C) 212.4
D) 637.2

Question 15

TABLE 11-1
Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, 40 undergraduates at Duke University participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his or her percentile score. Unknown to the subject, the test taker was a bogus student who was working with the researchers. The experimenters manipulated two factors: subject visibility and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of the test taker was either top 20% or bottom 20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) The data were subjected to appropriate analyses with the following results.

Referring to Table 11-1, in the context of this study, interpret the statement: "Subject visibility and test taker success interact."

A) The difference between the mean feedback time for visible and nonvisible subjects depends on the success of the test taker.
B) The difference between the mean feedback time for test takers scoring in the top 20% and bottom 20% depends on the visibility of the subject.
C) The relationship between feedback time and subject visibility depends on the success of the test taker.
D) All of the above are correct interpretations.

Question 16

In a one-way ANOVA, the null hypothesis is always

A) there is no treatment effect.
B) there is some treatment effect.
C) all the population means are different.
D) some of the population means are different.

Question 17

TABLE 11-2
An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

Referring to Table 11-2, the total degrees of freedom is

A) 3
B) 4
C) 16
D) 19

Question 18

Why would you use the Tukey-Kramer procedure?

A) to test for normality
B) to test for homogeneity of variance
C) to test independence of errors
D) to test for differences in pairwise means

Question 19

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, the within group sum of squares is

A) 1.0606.
B) 1.1825.
C) 3.1819.
D) 4.3644.

Question 20

Interaction in an experimental design can be tested in

A) a completely randomized model.
B) a two-factor model.
C) a Tukey-Kramer procedure.
D) all ANOVA models.

Question 21

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

A) Reject the null hypothesis because the p-value is smaller than the level of significance.
B) Reject the null hypothesis because the p-value is larger than the level of significance.
C) Do not reject the null hypothesis because the p-value is smaller than the level of significance.
D) Do not reject the null hypothesis because the p-value is larger than the level of significance.

Question 22

TABLE 11-5
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table:

Referring to Table 11-5, what was the total number of doctors included in the study?

A) 20
B) 40
C) 159
D) 160

Question 23

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, the critical value of Levene's test for homogeneity of variances at a 5% level of significance is

A) 0.64
B) 2.48
C) 3.29
D) 3.49

Question 24

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances at a 5% level of significance are, respectively,

A) 3, 12
B) 12, 3
C) 3, 15
D) 15, 3

Question 25

TABLE 11-4
A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

Referring to Table 11-4, the F test statistic for testing the main effect of types of signs is

A) 0.0109
B) 2.7844
C) 3.1742
D) 5.3176

Question 26

A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. How should the data be analyzed?

A) completely randomized design
B) randomized block design
C) 2 x 2 factorial design
D) Levene's test

Question 27

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

A) There is not sufficient evidence that the variances are all the same.
B) There is sufficient evidence that the variances are all the same.
C) There is not sufficient evidence that the variances are not all the same.
D) There is sufficient evidence that the variances are not all the same.

Question 28

TABLE 11-4
A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

Referring to Table 11-4, the within (error) degrees of freedom is

A) 1
B) 4
C) 8
D) 11

Question 29

TABLE 11-4
A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

Referring to Table 11-4, at 10% level of significance,

A) there is sufficient evidence to conclude that the difference between the mean traveling time for the different starting locations depends on the types of signs.
B) there is insufficient evidence to conclude that the difference between the mean traveling time for the different types of signs depends on the starting locations.
C) there is sufficient evidence to conclude that the difference between the mean traveling time for the different starting locations does not depend on the types of signs.
D) None of the above.

Question 30

TABLE 11-4
A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

Referring to Table 11-4, the degrees of freedom for the different building signs (factor A) is

A) 1
B) 2
C) 3
D) 8

Question 31

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, the null hypothesis for Levene's test for homogeneity of variances is

A) H₀ : μ_A = μ_B = μ_C = μ_D
B) H₀ : M_A = M_B = M_C = M_D
C) H₀ : σ_A² = σ_B² = σ_C² = σ_D²
D) H₀ : π_A = π_B = π_C = π_D

Question 32

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, the value of the test statistic for Levene's test for homogeneity of variances is

A) 0.25
B) 0.37
C) 4.36
D) 10.76

Question 33

TABLE 11-5
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table:

Referring to Table 11-5, what degrees of freedom should be used to determine the critical value of the F ratio against which to test for interaction between the two factors?

A) numerator df = 1, denominator df = 159
B) numerator df = 3, denominator df = 159
C) numerator df = 1, denominator df = 152
D) numerator df = 3, denominator df = 152

Question 34

TABLE 11-4
A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

Referring to Table 11-4, the F test statistic for testing the interaction effect between the types of signs and the starting location is

A) 0.0109
B) 2.7844
C) 3.1742
D) 5.3176

Question 35

TABLE 11-5
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table:

Referring to Table 11-5, interpret the test for interaction.

A) There is insufficient evidence to say at the 0.10 level of significance that the difference between the mean charges for foreign and USA graduates depends on primary specialty.
B) There is sufficient evidence to say at the 0.10 level of significance that the difference between the mean charges for foreign and USA graduates depends on primary specialty.
C) There is sufficient evidence at the 0.10 level of significance of a difference between the mean charges for foreign and USA medical graduates.
D) There is sufficient evidence to say at the 0.10 level of significance that mean charges depend on both primary specialty and medical school.

Question 36

TABLE 11-4
A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

Referring to Table 11-4, at 1% level of significance,

A) there is insufficient evidence to conclude that the difference between the mean traveling time for the different starting locations depends on the types of signs.
B) there is insufficient evidence to conclude that the difference between the mean traveling time for the different types of signs depends on the starting locations.
C) there is insufficient evidence to conclude that the relationship between traveling time and the types of signs depends on the starting locations.
D) All of the above.

Question 37

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, the p-value of the test statistic for Levene's test for homogeneity of variances is

A) 0.25
B) 0.64
C) 0.86
D) 3.49

Question 38

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3,

A) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not all the same.
B) at the 0.01 level of significance, the mean ratios for the 4 neighborhoods are all the same.
C) at the 0.10 level of significance, the mean ratios for the 4 neighborhoods are not significantly different.
D) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not significantly different from 0.

Question 39

TABLE 11-4
A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

Referring to Table 11-4, the mean squares for starting location (factor B) is

A) 48
B) 4,413.17
C) 12,288
D) 14,008.3

Question 40

TABLE 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
Interpret the results of the analysis summarized in the following table:
A) 3.
B) 4.
C) 12.
D) 16.
Answer:
A
Diff: 1
Referring to Table 11-3, the within group mean squares is

A) 0.0985.
B) 0.2910.
C) 1.0606.
D) 1.1825.

Question 41

The F test in a completely randomized model is just an expansion of the t test for independent samples.

Question 42

TABLE 11-5
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table:

Referring to Table 11-5, what degrees of freedom should be used to determine the critical value of the F ratio against which to test for differences in the mean charges for doctors among the four primary specialty areas?

A) numerator df = 1, denominator df = 159
B) numerator df = 3, denominator df = 159
C) numerator df = 1, denominator df = 152
D) numerator df = 3, denominator df = 152

Question 43

TABLE 11-5
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table:

Referring to Table 11-5, is there evidence of a difference between the mean charges of foreign and USA medical school graduates?

A) Yes, the test for the main effect for primary specialty is significant at α = 0.10.
B) No, the test for the main effect for medical school is not significant at α = 0.10.
C) No, the test for the interaction is not significant at α = 0.10.
D) Maybe, but we need information on the β-estimates to fully answer the question.

Question 44

A completely randomized design with 4 groups would have 6 possible pairwise comparisons.

Question 45

If you are comparing the average sales among 3 different brands you are dealing with a three-way ANOVA design.

Question 46

When the F test is used for ANOVA, the rejection region is always in the right tail.

Question 47

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the among group variation or SSA is ________.

Question 48

In a one-factor ANOVA analysis, the among sum of squares and within sum of squares must add up to the total sum of squares.

Question 49

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the null hypothesis that the average downhill coasting speeds of the 4 brands of bicycles are equal will be rejected at a level of significance of 0.05 if the value of the test statistic is greater than ________.

Question 50

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, construct the ANOVA table from the sample data.

Question 51

TABLE 11-5
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table:

Referring to Table 11-5, what degrees of freedom should be used to determine the critical value of the F ratio against which to test for differences between the mean charges of foreign and USA medical school graduates?

A) numerator df = 1, denominator df = 159
B) numerator df = 3, denominator df = 159
C) numerator df = 1, denominator df = 152
D) numerator df = 3, denominator df = 152

Question 52

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the within group variation or SSW is ________.

Question 53

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, in testing the null hypothesis that the average downhill coasting speeds of the 4 brands of bicycles are equal, the value of the test statistic is ________.

Question 54

TABLE 11-5
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. One theory is that Primary Specialty is an important factor in measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second factor which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. The president theorizes that foreign graduates will have higher mean charges than USA graduates. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the following table:

Referring to Table 11-5, what assumption(s) need(s) to be made in order to conduct the test for differences between the mean charges of foreign and USA medical school graduates?

A) There is no significant interaction effect between the area of primary specialty and the medical school on the doctors' mean charges.
B) The charges in each group of doctors sampled are drawn from normally distributed populations.
C) The charges in each group of doctors sampled are drawn from populations with equal variances.
D) All of the above are necessary assumptions.

Question 55

The analysis of variance (ANOVA) tests hypotheses about the population variance.

Question 56

In a two-factor ANOVA analysis, the sum of squares due to both factors, the interaction sum of squares and the within sum of squares must add up to the total sum of squares.

Question 57

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the value of MSA is ________, while MSW is ________.

Question 58

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the sporting goods retailer decided to perform an ANOVA F test. The amount of total variation or SST is ________.

Question 59

In a two-way ANOVA, it is easier to interpret main effects when the interaction component is not significant.

Question 60

The MSE must always be positive.

Question 61

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the null hypothesis should be rejected at a 5% level of significance.

Question 62

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

A) There is not sufficient evidence that the variances are all the same.
B) There is sufficient evidence that the variances are all the same.
C) There is not sufficient evidence that the variances are not all the same.
D) There is sufficient evidence that the variances are not all the same.

Question 63

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, what is the value of the test statistic for Levene's test for homogeneity of variances?

Question 64

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the test is valid only if the population of speeds is normally distributed.

Question 65

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, using an overall level of significance of 0.05, the critical range for the Tukey-Kramer procedure is ________.

Question 66

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that the 3 means other than the mean for Tornado are not significantly different from each other.

Question 67

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the test is robust to the violation of the assumption that the population of speeds is normally distributed.

Question 68

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the sporting goods retailer decided to compare the 4 treatment means by using the Tukey-Kramer procedure with an overall level of significance of 0.05. There are ________ pairwise comparisons that can be made.

Question 69

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the null hypothesis for Levene's test for homogeneity of variances is

A) H₀ : μ_A = μ_B = μ_C = μ_D
B) H₀ : M_A = M_B = M_C = M_D
C) H₀ : σ_A² = σ_B² = σ_C² = σ_D²
D) H₀ : π_A = π_B = π_C = π_D

Question 70

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

Question 71

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that there is a significant difference between all pairs of mean speeds.

Question 72

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

A) Reject the null hypothesis because the p-value is smaller than the level of significance.
B) Reject the null hypothesis because the p-value is larger than the level of significance.
C) Do not eject the null hypothesis because the p-value is smaller than the level of significance.
D) Do not reject the null hypothesis because the p-value is larger than the level of significance.

Question 73

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that the mean speed for the Tornado brand is significantly different from each of the mean speeds for other brands.

Question 74

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, what is the p-value of the test statistic for Levene's test for homogeneity of variances?

Question 75

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the decision made implies that all 4 means are significantly different.

Question 76

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that there is no significant difference between any pair of mean speeds.

Question 77

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the test is valid only if the population of speeds has the same variance for the 4 brands.

Question 78

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

Question 79

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, using an overall level of significance of 0.05, the critical value of the Studentized range Q used in calculating the critical range for the Tukey-Kramer procedure is ________.

Question 80

TABLE 11-6
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Referring to Table 11-6, the test is less sensitive to the assumption that the population of speeds has the same variance for the 4 brands if the sample sizes of the 4 brands are equal.