6 problems

Difficulty: Beginners

PDF of assignment is attached

***If problem states it has a table/chart it will be below the problem as you will see.***

Student: Dean Holleman
Date: 4/5/16

Course: QMBE 2786-001

Assignment: Homework# 6 – Chapter 11

1. Consider the partially completed one-way ANOVA summary table below.
a) Complete the remaining entries in the table.
b) How many population means are being tested?
c) Using ? = 0.05, what conclusions can be made concerning the
population means?
2

Source
Between
Within
Total

Click the icon to view a table of critical F-scores for ? = 0.05.

Sum of
Squares
?
36
110

Degrees of Freedom
2
?
8

a) Complete the ANOVA table below.
Source

Between

Sum of
Squares

Degrees of
Freedom
2

Mean Sum of
Squares

F

Within
36
Total
110
8
(Type integers or decimals. Round to three decimal places as needed.)
b) There are

population means being tested.

c) What are the hypotheses for this test?
A. H0: All the means are equal.

B. H0: None of the means are equal.

C. H0: Not all the means are equal.

D. H0: All the means are equal.

H1: None of the means are equal.
H1: All the means are equal.

H1: All the means are equal.

H1: Not all the means are equal.

Determine the critical F-score, F? , for this test.
F? =

(Round to three decimal places as needed.)

State the conclusion for ? = 0.05.
Since the F-test statistic is (1)

1: Table of Critical F-scores
Critical F-scores for ? = 0.05

than the critical F-score, (2)

the null hypothesis and conclude that (3)

Mean Sum of
Squares
?
?

F
?

2: Table of Critical F-scores
Critical F-scores for ? = 0.05

(1)

less

greater

(2)

reject

do not reject

(3)

all of the population means are the same.

at least one of the population means is different.

2. The data in the table show the number of pounds of bananas sold per week at a grocery store when the banana display was positioned in the produce, milk, and
cereal sections of the store.
a) Perform a one-way ANOVA using ? = 0.05 to determine if there is a difference in the average number of pounds of bananas sold per week in these three locations.
b) If warranted, perform a multiple comparison test to determine which pairs are different using ? = 0.05.
6 Click the icon to view the data.
7 Click the icon to view a table of critical F-scores for ? = 0.05.
8 Click the icon to view a studentized range table for ? = 0.05.
a) What are the correct hypotheses for the one-way ANOVA test?
A. H0: ?1 = ?2 = ?3

B. H0: ?1 ? ?2 ? ?3

C. H0: Not all the means are equal.

D. H0: ?1 = ?2 = ?3

H1: ?1 = ?2 = ?3

H1: Not all the means are equal.
H1: ?1 = ?2 = ?3

Complete the ANOVA summary table below.
Source

Between

Sum of
Squares

Degrees of
Freedom

H1: ?1 ? ?2 ? ?3

Mean Sum of
Squares

F

Within
Total

(Round to three decimal places as needed.)

Determine the critical F-score, F? , for this test.
F? =

(Round to three decimal places as needed.)

State the conclusion for ? = 0.05.
Since the F-test statistic is (1)
bananas sold (3)

b) Which means are different?
The means for (7)

than the critical F-score, (2)

different in these three locations.

the null hypothesis and conclude that the average number of pounds of

locations are different.

3: Number of Pounds of Bananas Sold

Pounds of Bananas Sold

Produce
41
48
30
39

4: Critical F-Scores

Table of Critical F-scores for ? = 0.05.

Milk
53
39
36
47
42

Cereal
27
35
33
37

5: Critical Values of the Studentized Range

Critical values of the studentized range for ? = 0.05.

6: Number of Pounds of Bananas Sold

Pounds of Bananas Sold

Produce
41
48
30
39

Milk
53
39
36
47
42

Cereal
27
35
33
37

7: Critical F-Scores

Table of Critical F-scores for ? = 0.05.

8: Critical Values of the Studentized Range

Critical values of the studentized range for ? = 0.05.

(1)
(7)

less

greater

(2)

reject

do not reject

(3)

none of the

the produce and milk

the produce and cereal and the milk and cereal
all of the

is

is not
the produce and milk and the milk and cereal
the produce and cereal
the milk and cereal

the produce and milk and the produce and cereal

3. Consider the accompanying partially completed randomized block ANOVA summary table. Complete parts a) through d) below.
12 Click the icon to view the partially completed ANOVA table.
Click here to view Page 1 of the table of critical F-distribution values.13
Click here to view Page 2 of the table of critical F-distribution values.14
a) Complete the remaining entries in the table.
Source

Between
Block
Error

Sum of
squares

Degrees of
freedom

144
72

3

Mean sum of
squares

F

6

Total
300
27
(Type integers or decimals rounded to two decimal places as needed.)
b) How many population means are being tested?

c) Using ? = 0.05, what conclusions can be made about the population means?
What are the correct null and alternative hypotheses?
A. H0 : All the population means are equal
H1 : All the population means are different
C. H0 : All the population means are different
H1 : All the population means are equal

B. H0 : Not all the population means are equal
H1 : All the population means are equal
D. H0 : All the population means are equal
H1 : Not all the population means are equal

What is the test statistic?
F =
x

(Type an integer or decimal rounded to two decimal places as needed.)

What is the critical value?
F? =

(Type an integer or decimal rounded to three decimal places as needed.)

What is the correct conclusion?
A. Reject H0 . There is not a significant difference between the means.

B. Do not reject H0 . There is not a significant difference between the means.
C. Reject H0 . There is a significant difference between the means.

D. Do not reject H0 . There is a significant difference between the means.

d) Was the blocking effective? Why or why not?

What are the correct null and alternative hypotheses?
A. H0 : All the ?BL 's are different
H1 : All the ?BL 's are equal

B. H0 : All the ?BL 's are equal
H1 : Not all the ?BL 's are equal

C. H0 : All the ?BL 's are equal

D. H0 : Not all the ?BL 's are equal

H1 : All the ?BL 's are different

H1 : All the ?BL 's are equal

What is the test statistic?
FBL =

(Type an integer or decimal rounded to two decimal places as needed.)

What is the critical value?
F? =

(Type an integer or decimal rounded to three decimal places as needed.)

What is the correct conclusion?
A. The blocking factor was not effective because H0 was rejected.

B. The blocking factor was effective because H0 was not rejected.

C. The blocking factor was not effective because H0 was not rejected.
D. The blocking factor was effective because H0 was rejected.

9: Partial ANOVA display
Source

Between

Sum of Degrees of
squares freedom

Block

144

Total

300

Error

10: Table of critical F-distribution values

72

3
6

27

Mean sum of
squares

F

11: Table of critical F-distribution values

12: Partial ANOVA display

Source

Between

Sum of Degrees of
squares freedom

Block

144

Total

300

Error

13: Table of critical F-distribution values

14: Table of critical F-distribution values

72

3
6

27

Mean sum of
squares

F

4. Researchers would like to investigate the impact that octane has on gas mileage. The accompanying table shows the gas mileage for six cars that were driven 1,000
miles with three different grades of gasoline, 87, 89, and 93 octane. The gas mileage was recorded for each octane level. Each car was tested with all three gasoline
grades. Complete parts a through c below.
17 Click the icon to view the data.
18 Click the icon to view a table of critical values for the studentized range.
a. Using ? = 0.05, does the octane level appear to have an effect on the gas mileage?

What are the correct hypotheses to test for differences in the mileage for the octane levels?
A. H0 : ?87 = ?89 = ?93
H1 : Not all the ?'s are equal.
C. H0 : Not all the ?'s are equal.
H1 : ?87 = ?89 = ?93

B. H0 : All the ?'s are different.
H1 : ?87 = ?89 = ?93
D. H0 : ?87 = ?89 = ?93
H1 : All the ?'s are different.

Determine the test statistic.
F =
x

(Round to two decimal places as needed.)

What is the p-value?
The p-value is
.
(Round to three decimal places as needed.)

State the conclusion about the population means.
(1)

H0 . Conclude that there is (2)

significant difference between the means.

b. Was the blocking effective? Why or why not?

What are the correct hypotheses to test for differences in the block means?
A. H0 : Not all the ?'s are equal.
H1 : ?A = ?B = ?C = ?D = ?E = ?F
C. H0 : All the ?'s are different.
H1 : ?A = ?B = ?C = ?D = ?E = ?F

B. H0 : ?A = ?B = ?C = ?D = ?E = ?F
H1 : Not all the ?'s are equal.
D. H0 : ?A = ?B = ?C = ?D = ?E = ?F
H1 : All the ?'s are different.

Determine the test statistic.
FBL =

(Round to two decimal places as needed.)

What is the p-value?
The p-value is
.
(Round to three decimal places as needed.)
State the conclusion about the blocking.
(3)

H0 . There (4)

evidence suggesting that the blocking was effective.

c. If warranted, determine which pairs of octanes were different using ? = 0.05.
The mileages for (9)

were significantly different.

Gas Mileage

Car

87 Octane

89 Octane

93 Octane

B

24.4

30.3

23.6

A

C
D
E
F

16: Critical Values of the Studentized Range

Critical values of the studentized range for ? = 0.05.

26.1
23.3
30.7
27.4
26.2

34.4
32.7
22.9
28.9
33.8

25.0
25.6
25.3
22.3
32.1

Gas Mileage

Car

87 Octane

89 Octane

93 Octane

B

24.4

30.3

23.6

A

C
D
E
F

26.1
23.3
30.7
27.4
26.2

34.4
32.7
22.9
28.9
33.8

25.0
25.6
25.3
22.3
32.1

18: Critical Values of the Studentized Range

Critical values of the studentized range for ? = 0.05.

(1)
(9)

Reject

Do not reject

(2)

no
a

(3)

Do not reject
Reject

(4)

is

is no

87 and 93 octane

87 and 89 octane and 87 and 93 octane

87 and 89, 87 and 93, and 89 and 93 octane

87 and 89 octane and 89 and 93 octane

87 and 89 octane

87 and 93 octane and 89 and 93 octane

none of the pairs

89 and 93 octane

5. Use the accompanying partially completed two-way ANOVA summary table to complete parts a through e below.
20

Click the icon to view the table.

a) Complete the two-way ANOVA table below.
Source

Factor A
Factor B

Interaction
Error

Sum of
Squares
160

Degrees of
Freedom
2

Mean Sum of
Squares

F

2

60

450

Total
770
(Type integers or decimals.)

45
53

b) How many replications are present for each cell?
r=
c) Using ? = 0.05, is there significant interaction between Factors A and B?

Identify the hypotheses for the interaction between Factors A and B. Choose the correct answer below.
A. H0 : Factor A and B do interact, H1 : Factor A and B do not interact
B. H0 : ?A = ?B , H1 : ?A ? ?B
C. H0 : ?A ? ?B , H1 : ?A = ?B

D. H0 : Factor A and B do not interact, H1 : Factor A and B do interact
Find the p-value for the interaction between Factors A and B.
p-value =

(Round to three decimal places as needed.)

Draw the appropriate conclusion for the interaction between Factors A and B. Choose the correct answer below.
A. Do not reject the null hypothesis. There is insufficient evidence to conclude that Factors A and B
interact.
B. Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is sufficient evidence to conclude that Factors A and B interact.

D. Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

d) Using ? = 0.05, are the Factor A means different?

Identify the hypotheses to test for Factor A. Choose the correct answer below.
A. H0 : ?A = ?B , H1 : ?A ? ?B

B. H0 : ?A1 = ?A2 = ?A3 , H1 : Not all Factor A means are equal
C. H0 : ?A1 ? ?A2 ? ?A3 , H1 : ?A1 = ?A2 = ?A3

D. H0 : ?A1 = ?A2 = ?A3 , H1 : ?A1 &gt; ?A2 &gt; ?A3
Find the p-value for Factor A.
p-value =

(Round to three decimal places as needed.)

Draw the appropriate conclusion for Factor A. Choose the correct answer below.
A. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all Factor A means
are equal.
B. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

C. Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor A means are
equal.
D. It is inappropriate to draw a conclusion from this test because the Factors A and B interact.

e) Using ? = 0.05, are the Factor B means different?

Identify the hypotheses to test for Factor B. Choose the correct answer below.
A. H0 : ?B1 ? ?B2 ? ?B3 , H1 : ?B1 = ?B2 = ?B3

B. H0 : ?B1 = ?B2 , H1 : Not all Factor B means are equal

C. H0 : ?B1 = ?B2 = ?B3 , H1 : Not all Factor B means are equal
D. H0 : ?A = ?B , H1 : ?A ? ?B
Find the p-value for Factor B.
p-value =

(Round to three decimal places as needed.)

Draw the appropriate conclusion for Factor B. Choose the correct answer below.
A. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all Factor B means
are equal.
C. Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor B means are

equal.
D. It is inappropriate to draw a conclusion from this test because the Factors A and B interact.

19: Partially completed two-way ANOVA summary table
Source

Factor A
Factor B

Interaction
Error

Total

Sum of Degrees of
Squares Freedom
160
60

450
770

2

Mean Sum of
Squares

F

2
45
53

20: Partially completed two-way ANOVA summary table
Source

Factor A
Factor B

Interaction
Error

Total

Sum of Degrees of
Squares Freedom
160
60

450
770

2
2

45
53

Mean Sum of
Squares

F

6. Suppose the school of business at a university would like to compare the starting salaries for both men and women who graduated with different majors. The
accompanying data show starting salaries for random students from the most recent graduating class. Complete parts a through e below.
24 Click the icon to view the data table.
a) Using ? = 0.05, is there significant interaction between Factor A and Factor B (major and gender)?

Identify the hypotheses for the interaction between major and gender. Choose the correct answer below.
A. H0 : ?Major = ?Gender , H1 : ?Major ? ?Gender
B. H0 : ?Major ? ?Gender , H1 : ?Major = ?Gender

C. H0 : Major and gender do interact, H1 : Major and gender do not interact
D. H0 : Major and gender do not interact, H1 : Major and gender do interact
Find the p-value for the interaction between major and gender.
p-value =

(Round to three decimal places as needed.)

Draw the appropriate conclusion for the interaction between major and gender. Choose the correct answer below.
A. Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

C. Do not reject the null hypothesis. There is insufficient evidence to conclude that major and gender
interact.

D. Reject the null hypothesis. There is sufficient evidence to conclude that major and gender interact.

b) Using two-way ANOVA and ? = 0.05, does the major have an effect on a person's starting salary?
Identify the hypotheses to test for the effect of major. Choose the correct answer below.
A. H0 : ?Finance = ?Marketing = ?Accounting , H1 : ?Finance &gt; ?Marketing &gt; ?Accounting
B. H0 : ?Major = ?Gender , H1 : ?Major ? ?Gender

C. H0 : ?Finance = ?Marketing = ?Accounting , H1 : Not all major means are equal

D. H0 : ?Finance ? ?Marketing ? ?Accounting , H1 : ?Finance = ?Marketing = ?Accounting
Find the p-value for the effect of major.
p-value =

(Round to three decimal places as needed.)

Draw the appropriate conclusion for the effect of major. Choose the correct answer below.
A. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all major means
are equal.

C. Reject the null hypothesis. There is sufficient evidence to conclude that not all major means are equal.
D. It is inappropriate to analyze because major and gender interact.

c) Using two-way ANOVA and ? = 0.05, does gender have an effect on a person's starting salary?
Identify the hypotheses to test for the effect of gender. Choose the correct answer below.
A. H0 : ?Major = ?Gender , H1 : ?Major ? ?Gender

B. H0 : ?Women = ?Men , H1 : Not all gender means are equal
C. H0 : ?Women ? ?Men , H1 : ?Women = ?Men

D. H0 : ?Finance = ?Marketing = ?Accounting , H1 : Not all gender means are equal
Find the p-value for the effect of gender.
p-value =

(Round to three decimal places as needed.)

Draw the appropriate conclusion for the effect of gender. Choose the correct answer below.
A. Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.

B. Reject the null hypothesis. There is sufficient evidence to conclude that not all gender means are equal.
C. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all gender means
are equal.
D. It is inappropriate to analyze because major and gender interact.

d) If warranted, determine which means are significantly different using ? = 0.05.
Are the means for the finance and marketing majors significantly different?
A. No

B. Yes

C. The comparison is unwarranted because there is insufficient evidence to conclude that not all major
means are equal.
D. The comparison is unwarranted because major and gender interact.

Are the means for the finance and accounting majors significantly different?

A. No

B. Yes

C. The comparison is unwarranted because there is insufficient evidence to conclude that not all major
means are equal.
D. The comparison is unwarranted because major and gender interact.

Are the means for the marketing and accounting majors significantly different?
A. No

B. Yes

C. The comparison is unwarranted because there is insufficient evidence to conclude that not all major
means are equal.
D. The comparison is unwarranted because major and gender interact.
Are the means for women and men significantly different?
A. No, because there is insufficient evidence to conclude that not all gender means are equal.
B. Yes, because there is sufficient evidence to conclude that not all gender means are equal.
C. No, because there is sufficient evidence to conclude that not all gender means are equal.
D. The comparison is unwarranted because major and gender interact.

e) Construct an interaction plot for the major and gender factors. Choose the correct plot below.

55,000

Women
Men

50,000
45,000
40,000

F

M

Major

A

B.

Interaction Between
Major and Gender

55,000

Women
Men

50,000
45,000
40,000

21: Starting salaries for random students

F

M

Major

A

C.

Starting Salary (\$)

Interaction Between
Major and Gender

Starting Salary (\$)

Starting Salary (\$)

A.

Interaction Between
Major and Gender

55,000

Women
Men

50,000
45,000
40,000

F

M

Major

A

Women

Finance
45,900
46,500
47,600

Men

44,700
48,700
50,400
41,900
53,600

Marketing Accounting
41,600

53,400

40,900

49,900

43,800
44,700
43,200
41,300
42,500
39,100

22: Studentized range table (0.05 level)

42,500
55,500
45,600
52,800
46,800
47,800

23: Studentized range table (0.01 level)

24: Starting salaries for random students

Women

Finance
45,900
46,500
47,600

Men

44,700
48,700
50,400
41,900
53,600

Marketing Accounting
41,600

53,400

40,900

49,900

43,800
44,700
43,200
41,300
42,500
39,100

25: Studentized range table (0.05 level)

42,500
55,500
45,600
52,800
46,800
47,800

26: Studentized range table (0.01 level)