Question

In: Math

Television advertisers base their investment decisions regarding the promotion of their products and services on demographic...

Television advertisers base their investment decisions regarding the promotion of their products and services on demographic information about television viewers. The age of the viewers is a key factor in their process. The following table shows the number of hours that a random sample of individuals watched television during the week. The individuals are grouped according to their ages. Minitab is required. You will need to enter the data into Minitab.

Age Group

18-24

25-34

35-49

50-64

49

41

44

39

33

40

19

14

33

33

27

15

39

35

36

17

71

21

49

20

a. At the 0.05 level of significance, determine if there is a difference in the mean number of hours of television watched by age group. State your hypotheses and show all 7 steps clearly. (14 points)

b. Give and interpret the p-value. (3 points)

c. Should Tukey pairwise comparisons be conducted? Why or why not? (3 points)

d. If appropriate, use Minitab to produce Tukey pairwise comparison. Write a few sentences with your conclusions from those comparisons. (4 points)

e. Use Levene’s test to determine if the assumption of homogeneity of variances is valid. Give the hypotheses, test statistic, p-value, decision, and conclusion. Use the 0.05 level of significance. (8 points)

f. Verify with Minitab by attaching or including relevant output. (6 points)

Solutions

Expert Solution

a. At the 0.05 level of significance, determine if there is a difference in the mean number of hours of television watched by age group. State your hypotheses and show all 7 steps clearly. (14 points)

One-way ANOVA: 18-24, 25-34, 35-49, 50-64

Method

Null hypothesis

All means are equal

Alternative hypothesis

Not all means are equal

Significance level

α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor

Levels

Values

Factor

4

18-24, 25-34, 35-49, 50-64

Analysis of Variance

Source

DF

Adj SS

Adj MS

F-Value

P-Value

Factor

3

1454

484.6

3.38

0.044

Error

16

2296

143.5

Total

19

3750

Model Summary

S

R-sq

R-sq(adj)

R-sq(pred)

11.9791

38.77%

27.29%

4.33%

Means

Factor

N

Mean

StDev

95% CI

18-24

5

45.00

15.94

(33.64, 56.36)

25-34

5

34.00

8.00

(22.64, 45.36)

35-49

5

35.00

12.23

(23.64, 46.36)

50-64

5

21.00

10.32

(9.64, 32.36)

Pooled StDev = 11.9791

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor

N

Mean

Grouping

18-24

5

45.00

A

35-49

5

35.00

A

B

25-34

5

34.00

A

B

50-64

5

21.00

B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference of
Levels

Difference
of Means

SE of
Difference

95% CI

T-Value

Adjusted
P-Value

25-34 - 18-24

-11.00

7.58

(-32.70, 10.70)

-1.45

0.487

35-49 - 18-24

-10.00

7.58

(-31.70, 11.70)

-1.32

0.564

50-64 - 18-24

-24.00

7.58

(-45.70, -2.30)

-3.17

0.027

35-49 - 25-34

1.00

7.58

(-20.70, 22.70)

0.13

0.999

50-64 - 25-34

-13.00

7.58

(-34.70, 8.70)

-1.72

0.348

50-64 - 35-49

-14.00

7.58

(-35.70, 7.70)

-1.85

0.288

Individual confidence level = 98.87%

Critical value of F(3,16) at 0.05 level of significance = 3.239

Calculated F=3.38 > critical F value 3.239. Ho is rejected.

Calculated F=3.38, P=0.044 which is < 0.05 level of significance. Ho is rejected. We conclude that there is a difference in the mean number of hours of television watched by age group.

b. Give and interpret the p-value. (3 points)

P=0.044.

P value is observing this much difference between groups or more when the null hypothesis is true.

c. Should Tukey pairwise comparisons be conducted? Why or why not? (3 points)

since ANOVA is significant pairwise comparisons to be conducted to see which pairs are significant.

d. If appropriate, use Minitab to produce Tukey pairwise comparison. Write a few sentences with your conclusions from those comparisons. (4 points)

Tukey Simultaneous Tests for Differences of Means

Difference of
Levels

Difference
of Means

SE of
Difference

95% CI

T-Value

Adjusted
P-Value

25-34 - 18-24

-11.00

7.58

(-32.70, 10.70)

-1.45

0.487

35-49 - 18-24

-10.00

7.58

(-31.70, 11.70)

-1.32

0.564

50-64 - 18-24

-24.00

7.58

(-45.70, -2.30)

-3.17

0.027

35-49 - 25-34

1.00

7.58

(-20.70, 22.70)

0.13

0.999

50-64 - 25-34

-13.00

7.58

(-34.70, 8.70)

-1.72

0.348

50-64 - 35-49

-14.00

7.58

(-35.70, 7.70)

-1.85

0.288

Individual confidence level = 98.87%

The age groups 50-64 and 18-24 are significant. All other pairs are not significant.

e. Use Levene’s test to determine if the assumption of homogeneity of variances is valid. Give the hypotheses, test statistic, p-value, decision, and conclusion. Use the 0.05 level of significance. (8 points)

Null hypothesis

All variances are equal

Alternative hypothesis

At least one variance is different

Significance level

α = 0.05

Tests

Method

Test
Statistic

P-Value

Multiple comparisons

0.650

Levene

0.45

0.721

Calculated test value 0.45, P=0.721 which is > 0.05 level. Ho is not rejected.

We conclude that assumption of homogeneity of variances is valid.


Related Solutions

describe the decisions of Patagonia’s company make regarding their individual products and services, product lines and...
describe the decisions of Patagonia’s company make regarding their individual products and services, product lines and product mixes?
Describe the decisions companies usually take regarding their individual products and services, product lines, and product...
Describe the decisions companies usually take regarding their individual products and services, product lines, and product mixes
Describe the framework that consumer normally follows in making decisions regarding the purchase of products or...
Describe the framework that consumer normally follows in making decisions regarding the purchase of products or services. Discuss the difficulties that consumer encounter with the application of that framework when purchasing financial services. Explain what heuristics are, and using any three of the heuristics discuss how they utilized in the decision making process for a consumer.
Company DEF needs advice regarding its investment decisions. Investment alternative A which the company is currently...
Company DEF needs advice regarding its investment decisions. Investment alternative A which the company is currently evaluating is a new machine with an initial outlay of $2,000,000, economic life of 4 years and no residual value. The machine will be related to an incremental annual revenue of $1,000,000 and incremental annual costs of $320,000. The machine will be depreciated on a straight-line basis. Some time ago, DEF has issued bonds with total face value of $18,000,000 which pay annual coupons...
Company DEF needs advice regarding its investment decisions. Investment alternative A which the company is currently...
Company DEF needs advice regarding its investment decisions. Investment alternative A which the company is currently evaluating is a new machine with an initial outlay of $2,000,000, economic life of 4 years and no residual value. The machine will be related to an incremental annual revenue of $1,000,000 and incremental annual costs of $320,000. The machine will be depreciated on a straight-line basis. Some time ago, DEF has issued bonds with total face value of $18,000,000 which pay annual coupons...
Credit unions decisions making process regarding its product and services due to the current Pandemic situation....
Credit unions decisions making process regarding its product and services due to the current Pandemic situation. Required: 1) Give examples using this context, of each step in the decision-making process as described in Unit 6. 2) Your project must include but is not limited to the following: a) A summary of the nature and history of the company. b) Background elements of the decision selected and what circumstances have resulted in the decision needing to be made. c) The possible...
Regarding Capital Expenditure Decisions, how does a manager go about evaluating an investment proposal? (from Ch...
Regarding Capital Expenditure Decisions, how does a manager go about evaluating an investment proposal? (from Ch 16 of Managerial Accounting: Creating Value in a Dynamic Business Environment (10th Edition)
(A) write an introduction to corporate and merchant/ investment banking products and services (two paragraphs) (B)...
(A) write an introduction to corporate and merchant/ investment banking products and services (two paragraphs) (B) outline, explain and discuss these products and services. (D) explain the advantages and disadvantages of the products to the clients.  
Retirement Investment Products (RIP) offers a full complement of retirement planning services and a diverse line...
Retirement Investment Products (RIP) offers a full complement of retirement planning services and a diverse line of retirement investments that have varying degrees of risk. With the investment products available at RIP, investors could form retirement funds with any level of risk preferred—from risk-free to extremely risky. RIP’s reputation in the investment community is impeccable because the service agents who advise clients are required to fully inform their clients of the risk possibilities that exist for any investment position, whether...
Puget World, Inc., manufactures two models of television sets, the N 800 XL model and the N 500 model. Data regarding the two products follow:
  Puget World, Inc., manufactures two models of television sets, the N 800 XL model and the N 500 model. Data regarding the two products follow:   Direct Labor-Hours per Unit Annual Production Total DirectLabor-Hours   Model N 800 XL 2.5   3,500 units 8,750   Model N 500 1.3 12,500 units 16,250               25,000           Additional information about the company follows: a. Model N 800 XL requires $65 in direct materials per...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT