Deck 13: Analysis of Variance Anova

Question 1

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Analysis of Kevin's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the appropriate decision is ___.

A) inconclusive
B) reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃
C) reject the null hypothesis $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
D) do not reject the null hypothesis $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$$\mu$ ₃
E) do not reject the null hypothesis $\mu$ ₁ $\le$$\mu$ ₂ $\le$ $\mu$ ₃

Answer 1

reject the null hypothesis $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃

Question 2

In analysis of variance tests a F distribution forms the basis for making the decisions.

Answer 2

True

Question 3

Analysis of variance may be used to test the differences in the means of more than two independent populations.

Answer 3

True

Question 4

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (colour neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Analysis of Kevin's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the observed F value is ___.

A) 0.5022
B) 0.1333
C) 1.9911
D) 17.5100
E) 22.4567

Question 5

The statistical methods of analysis of variance assume that the populations are normally distributed.

Question 6

Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy, claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the critical F value is ___.

A) 13.68
B) 19.43
C) 3.59
D) 19.45
E) 3.68

Question 7

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. Cindy's null hypothesis is ___.

A) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃ = $\mu$ ₄ = $\mu$ ₅

B) $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃ $\neq$$\mu$ ₄ $\neq$$\mu$ ₅

C) $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃ $\neq$$\mu$ ₄

D) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃ = $\mu$ ₄

E) $\mu$ ₁ $\neq$ $\mu$ ₂= $\mu$ ₃ = $\mu$ ₄

Question 8

Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy, claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the observed F value is ___.

A) 16738.1
B) 1769.75
C) 33476.19
D) 26546.18
E) 9.457912

Question 9

Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy, claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the appropriate decision is ___.

A) reject the null hypothesis $\mu$ ₁ = $\mu$ ₂= $\mu$ ₃
B) reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃
C) do not reject the null hypothesis $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$$\mu$ ₃
D) do not reject the null hypothesis $\mu$ ₁ $\le$$\mu$ ₂ $\le$ $\mu$ ₃
E) inconclusive

Question 10

Pate's Pharmacy, Inc. operates a regional chain of 120 pharmacies. Each pharmacy's floor plan includes a greeting card department which is relatively isolated. Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department. She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level. Analysis of Sandra's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the observed F value is ___.

A) 0.5022
B) 0.1333
C) 1.9911
D) 7.5000
E) 1.000

Question 11

Pate's Pharmacy, Inc. operates a regional chain of 120 pharmacies. Each pharmacy's floor plan includes a greeting card department which is relatively isolated. Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department. She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level. Analysis of Sandra's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the appropriate decision is ___.

A) do not reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$ $\mu$ ₃
B) do not reject the null hypothesis $\mu$ ₁ = $\mu$ ₂= $\mu$ ₃
C) reject the null hypothesis $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$$\mu$ ₃
D) reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃
E) inclusive

Question 12

Pate's Pharmacy, Inc. operates a regional chain of 120 pharmacies. Each pharmacy's floor plan includes a greeting card department which is relatively isolated. Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department. She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level. Analysis of Sandra's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the critical F value is ___.

A) 13.68
B) 19.43
C) 3.59
D) 19.45
E) 3.68

Question 13

A completely randomized design has been analyzed by using a one-way ANOVA. There are three treatment groups in the design, and each sample size is four. The mean for group 1 is 25.00 and for group 3 it is 27.50. MSE is 3.19. Using α=0.05 there is a significant difference between these two groups.

Question 14

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (colour neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Analysis of Kevin's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the critical F value is ___.

A) 3.57
B) 19.43
C) 3.68
D) 19.45
E) 2.85

Question 15

The statistical methods of analysis of variance assume equal sample means.

Question 16

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table: Using $\alpha$ = 0.01, the appropriate decision is ___.

A) reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄

B) reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃ $\neq$ $\mu$ ₄

C) do not reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄= $\mu$ ₅

D) do not reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃ $\neq$ $\mu$ ₄ $\neq$$\mu$ ₅

E) do nothing

Question 17

Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy, claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Kathleen's null hypothesis is ___.

A) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
B) $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$$\mu$ ₃
C) $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$$\mu$ ₃
D) $\mu$ ₁ $\le$$\mu$ ₂ $\le$$\mu$ ₃
E) $\mu$ ₁ $\le$ $\mu$ ₂ ≥ $\mu$ ₃

Question 18

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (colour neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Analysis of Kevin's data yielded the following ANOVA table: Using $\alpha$ = 0.05, the appropriate decision is ___.

A) do not reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃
B) do not reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$ $\mu$ ₃
C) reject the null hypothesis $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$$\mu$ ₃
D) reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃
E) do nothing

Question 19

BigShots, Inc. is a specialty e-tailer that operates 87 catalogue websites on the Internet. Kevin Conn, Sales Director, feels that the style (colour scheme, graphics, fonts, etc.) of a website may affect its sales. He chooses three levels of design style (neon, old world, and sophisticated) and randomly assigns six catalogue websites to each design style. Kevin's null hypothesis is ___.

A) $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$ $\mu$ ₃
B) $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃
C) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
D) $\mu$ ₁ $\le$$\mu$ ₂ $\le$ $\mu$ ₃
E) $\mu$ ₁ $\le$ $\mu$ ₂ ≥ $\mu$ ₃

Question 20

Determining the table value for the F distribution requires two values for degrees of freedom.

Question 21

For the following ANOVA table, the df_Error value is ___.

A) 4
B) 20
C) 12
D) 64
E) 16

Question 22

For the following ANOVA table, the MS Error value is ___.

A) 20
B) 60
C) 800
D) 2
E) 200

Question 23

For the following ANOVA table, the observed F value is ___.

A) 0.67
B) 1.50
C) 6.00
D) 5.00
E) 4.00

Question 24

For the following ANOVA table, the MS Error value is ___.

A) 4,320
B) 372
C) 348
D) 30
E) 4

Question 25

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table: Using $\alpha$ = 0.01, the appropriate decision is ___.

A) reject the null hypothesis $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃ = $\mu$ ₄

B) reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃ $\neq$ $\mu$ ₄

C) do not reject the null hypothesis $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃ = $\mu$ ₄

D) do not reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃ $\neq$ $\mu$ ₄

E) do nothing

Question 26

Data on three treatment levels are shown in the following table: For a one-way ANOVA, the Between Sum of Squares (SSB) is ___.

A) 36.17
B) 28.75
C) 64.92
D) 18.03
E) 28.04

Question 27

Data on three treatment levels are shown in the following table: For a one-way ANOVA, the Error Sum of Squares (SSE) is ___.

A) 36.17
B) 28.75
C) 64.92
D) 18.03
E) 28.04

Question 28

Data on three treatment levels are shown in the following table: For a one-way ANOVA using  = 0.05, the critical F value is ___.

A) 3.86
B) 3.59
C) 19.38
D) 4.26
E) 6.8

Question 29

As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Your null hypothesis is ___.

A) $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃

B) $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$ $\mu$ ₃

C) $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃

D) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃

E) $\mu$ ₁ $\le$ $\mu$ ₂ $\ge$$\mu$ ₃

Question 30

Data on three treatment levels are shown in the following table: For a one-way ANOVA using $\alpha$ = 0.05, the observed F value is ___.

A) 5.66
B) 3.19
C) 18.08
D) 4.34
E) 8.98

Question 31

As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Analysis of the data yielded the following ANOVA table: Using $\alpha$ = 0.05, the critical F value is ___.

A) 3.68
B) 3.74
C) 4.54
D) 4.60
E) 9.46

Question 32

For the following ANOVA table, the MS Treatment value is ___.

A) 150
B) 50
C) 450
D) 3.49
E) 40

Question 33

For the following ANOVA table, the observed F value is ___.

A) 0.5625
B) 50
C) 25
D) 0.02
E) 0.09

Question 34

As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Your alternative hypothesis is ___.

A) $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃

B) $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$ $\mu$ ₃

C) $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃

D) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃

E) at least one of the means is different from the others

Question 35

Data on three treatment levels are shown in the following table: For a one-way ANOVA using $\alpha$ = 0.05, the appropriate decision is ___.

A) do not reject the null hypothesis $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$ $\mu$ ₃

B) do not reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃

C) reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃

D) reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃

E) do not reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃

Question 36

For the following ANOVA table, the MS Treatment value is ___.

A) 20
B) 200
C) 76
D) 84
E) 360

Question 37

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table: Using $\alpha$ = 0.01, the critical F value is ___.

A) 5.33
B) 6.21
C) 0.16
D) 5.29
E) 6.89

Question 38

Data on three treatment levels are shown in the following table: For a one-way ANOVA, the Total Sum of Squares (SST) is ___.

A) 36.17
B) 28.75
C) 64.92
D) 18.03
E) 28.04

Question 39

Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table: Using $\alpha$ = 0.01, the observed F value is ___.

A) 6.2102
B) 0.1610
C) 0.1875
D) 5.3333
E) 4.9873

Question 40

For the following ANOVA table, the df_Treatment value is ___.

A) 3
B) 43
C) 1.15
D) 460
E) 150

Question 41

As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Analysis of the data yielded the following ANOVA table: Using $\alpha$ = 0.05, the observed F value is ___.

A) 60022.37
B) 16738.1
C) 1769.745
D) 9.457912
E) 18

Question 42

As director of the employee wellness and productivity program in your company, you are interested in comparing the effects of strength training, aerobic training, and yoga on decreasing rates of injury and absenteeism. The company has 9 divisions with roughly the same number of employees, and you randomly assign 3 divisions to participate in strength training, 3 to aerobic training, and 3 to yoga. Analysis of the data yielded the following ANOVA table: Using $\alpha$ = 0.05, the appropriate decision is ___.

A) reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃

B) do not reject the null hypothesis $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$ $\mu$ ₃

C) reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃

D) do not reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃

E) inconclusive

Question 43

In an experiment where the means of 6 groups are being tested 2 at a time, ___ tests are conducted. If each test is analyzed using α = 0.01, the probability that at least 1 Type I error will be committed is ___.

A) 12; 0.12
B) 12; 0.88
C) 15; 0.14
D) 15; 0.86
E) 36; 0.30

Question 44

Complete the following two-factor ANOVA table. Determine the critical F values and reach conclusions about the hypotheses for effects at 5% significance level.

Question 45

A large company buys thousands of lightbulbs every year. The company is currently considering four brands of lightbulbs to choose from and wants to investigate if the mean lifetimes of the 4 types of bulbs are the same. The research department randomly selected 7 bulbs of each type and test how long they lasted until they burned out. The research department then analyzed the data and obtained the following ANOVA table:

a) Fill in the blanks of the partially completed ANOVA table.
b) At test whether there are differences in the mean lifetimes of the four brands of lightbulbs.