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11.13 A management consulting company presents a three-day seminar on project ma

ID: 3182718 • Letter: 1

Question

11.13 A management consulting company presents a three-day seminar on project management to various clients. The seminar is basically the same each time it is given. However, sometimes it is presented to high-level managers, sometimes to midlevel managers, and sometimes to low-level managers. The seminar facilitators believe evaluations of the seminar may vary with the audience. Suppose the following data are randomly selected evaluation scores from different levels of managers who attend the seminar. The ratings on a scale from 1 to 10, with 10 being the highest. Use a one-way ANOVA to determine whether there is a significant difference in the evaluations according to manager level. Assume alpha= 0.05.

High Level             Mid Level              Low Level

7                           8                            5

7                           9                            6

8                           8                            5

7                           10                          7

9                           9                            4

                            10                           8

                            8

1) please set up ANOVA test

(If you do not have ANOVA table for 11.13, use

SSC=53.37, SSE=22.657 and rests are easily obtained.)

2) write down conclusion using CV and p-value approach

3) write down implication

4) set up Tukey table

(Note: Last column of Tukey table should be one of two, same or not same)

                          

Explanation / Answer

Solution:

Part 1

From the given data, the ANOVA table is calculated as below:

No

X1

X2

X3

X1^2

X2^2

X3^2

1

7

8

5

49

64

25

2

7

9

6

49

81

36

3

8

8

5

64

64

25

4

7

10

7

49

100

49

5

9

9

4

81

81

16

6

10

8

100

64

7

8

64

Total

38

62

35

292

554

215

ANOVA

Source of Variation

SS

df

MS

F

P-value

F critical

Between Groups

29.61

2

29.61/2 = 14.80

14.80/1.26 = 11.76

0.001

3.68

Within Groups

18.89

15

18.89/15 = 1.26

Total

48.5

17

Part 2

The critical value is given as below:

Critical value = 3.68 (By using excel)

Test statistic F = 11.76

Test statistic F > Critical value

So, we reject the null hypothesis that the average values for high level, mid level and low level are same. Now, we have to see p-value approach given as below:

P-value = 0.001

Alpha value = 0.05

P-value < Alpha value

So, according to decision rule, we reject the null hypothesis that the average values for high level, mid level and low level are same.

Part 3

This one way ANOVA implies that there is a significant difference in the average ratings for the given three levels.

Part 4

The Tukey table for comparison of means is given as below:

Multiple Comparisons

(I) Level

(J) Level

Mean Difference (I-J)

Std. Error

Sig.

High Level

Mid Level

-1.25714

.65710

.169

Low Level

1.76667*

.67953

.050

Mid Level

High Level

1.25714

.65710

.169

Low Level

3.02381*

.62434

.001

Low Level

High Level

-1.76667*

.67953

.050

Mid Level

-3.02381*

.62434

.001

No

X1

X2

X3

X1^2

X2^2

X3^2

1

7

8

5

49

64

25

2

7

9

6

49

81

36

3

8

8

5

64

64

25

4

7

10

7

49

100

49

5

9

9

4

81

81

16

6

10

8

100

64

7

8

64

Total

38

62

35

292

554

215