Worksheet 11 (chapter11)

4/7/2020 Worksheet #11 (Chapter 11)

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1.

2.

Student: _____________________

Date: _____________________

Instructor: Jeremy Mandelkern

Course: MyLab Statistic for Basic

Business Statistics, 14th Edition

Assignment: Worksheet #11 (Chapter

11)

Consider an experiment with groups, with values in each.eight two

a. How many degrees of freedom are there in determining the among-group variation?

b. How many degrees of freedom are there in determining the within-group variation?

c. How many degrees of freedom are there in determining the total variation?

a. There is/are degree(s) of freedom in determining the among-group variation.

(Simplify your answer.)

b. There is/are degree(s) of freedom in determining the within-group variation.

(Simplify your answer.)

c. There is/are degree(s) of freedom in determining the total variation.

(Simplify your answer.)

Consider an experiment with

groups, with values

in each. For the ANOVA

summary table shown to the

right, fill in all the missing

results.

three seven Source

Degrees of

Freedom

Sum of

Squares

Mean Square

(Variance) F

Among

groups ?c − 1 = SSA ?= MSA = 115 ?FSTAT =

Within

groups ?n − c = SSW = 414 MSW ?=

Total ?n − 1 = SST ?=

Complete the ANOVA summary table below.

Source Degrees of Freedom Sum of Squares

Mean Square

(Variance) F

Among groups c − 1 = SSA = MSA = 115 FSTAT =

Within groups n c− = SSW = 414 MSW =

Total n − 1 = SST =

(Simplify your answers.)

4/7/2020 Worksheet #11 (Chapter 11)

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3.

1: Brand Valuation Results

A research assistant compared brand values for three sectors in a study of 100 global brands: the financial institution

sector, the technology sector, and the telecom sector. The research assistant findings are in the accompanying table.

Complete parts (a) through (c) below.

Click here to view the results of the study.1

Click here to view a partial table of critical values of the Studentized Range, Q.2

a. Complete the ANOVA summary table.

Source

Degrees of

Freedom Sum of Squares Mean Squares F

Among groups 2 927,116.40

Within groups 46 10,251,767.92

Total 48 11,178,884.32

(Type integers or decimals rounded to two decimal places as needed.)

b. At the level of significance, is there evidence of a difference in mean brand value among the sectors?0.05

Determine the hypotheses. Choose the correct answer below.

A. H0: 123

= =

H1: Not all are equal

j

(where j 1,2,3)=

B. H0: 123

≠ ≠

H1: 1 2 3

= =

C. H0: 123

= =

H1: 123

≠ ≠

D. H0: Not all are equal

j

(where j 1,2,3)=

H1: 1 2 3

= =

Determine the p-value.

p-value (Round to three decimal places as needed.)=

Since the p-value is (1) than the level of significance, (2) . There is

(3) evidence to conclude that there is a difference in mean brand value among the sectors.

0.05 H0

c. If the results in (b) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which sectors differ

in mean rating. Discuss your findings.

At the level of significance, for which sectors is there enough evidence to conclude that the mean ratings differ?

Select all that apply.

0.05

A. There is a significant difference in mean brand value between technology brands and telecom

brands.

B. There is a significant difference in mean brand value between financial institutions and telecom

brands.

C. There is a significant difference in mean brand value between financial institutions and

technology brands.

D. Because there is no significant difference among the groups, the Tukey-Kramer procedure is

not appropriate.

4/7/2020 Worksheet #11 (Chapter 11)

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2: Critical values of the Studentized Range, Q

(1) less

greater

(2) reject

do not reject

(3) insufficient

sufficient

Source

Degrees of

Freedom Sum of Squares

Mean

Squares F

Among groups 2 927,116.40

Within groups 46 10,251,767.92

Total 48 11,178,884.32

Group N Mean

Financial Institution 22 24,368.77

Technology 16 61,045.34

Telecom 11 37,477.73

4/7/2020 Worksheet #11 (Chapter 11)

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4.

A pet food company conducted an experiment to compare different cat foods. A sample of cats from the

population at a local animal shelter was selected. Six cats were randomly assigned to each of the five products. Each

was then presented with 3 ounces of the selected food in a dish at feeding time. The researchers defined the variable

to be measured as the number of ounces of food that the cat consumed within a 10-minute time interval. The results

for this experiment are summarized in the accompanying table. Complete (a) through (d) below.

five 30

Click on the icon to view the results.

3

Click on the icon to view a partial table of critical values of F.

4

Click on the icon to view a partial table of critical values of the Studentized Range, Q.

5

a. At the level of significance, is there evidence of a difference in the mean amount of food eaten among the

various products?

0.05

Determine the hypotheses. Choose the correct answer below.

A. H0: 1 2

= = • • • = 6

H1: Not all are equal

j

(where j 1,2, …, )= 6

B. H0: 1 2

= = • • • = 5

H1: Not all are equal

j

(where j 1,2, …, )= 5

C. H0: 1 2

= = • • • = 5

H1: 1 2

≠ ≠ • • • ≠ 5

D. H0: 1 2

= = • • • = 6

H1: 1 2

≠ ≠ • • • ≠ 6

Find the test statistic.

FSTAT (Round to two decimal places as needed.)=

Determine the critical value.

F (Round to two decimal places as needed.)=

Reach a decision.

(1) H0. There is (2) evidence of a difference in the mean amount of food eaten

among the various products.

b. If appropriate, determine which products differ in the mean amount of food eaten.

Let the kidney-based cat food be group 1, the shrimp-based cat food be group 2, the chicken liver-based cat food be

group 3, the salmon-based cat food be group 4, and the beef-based cat food be group 5.

Is there significant evidence that group 1 and group 2 differ in the mean amount of food eaten?

A. No

B. Yes