Question

The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals who are in marketing. Three groups are considered: management, research and advertising (higher scores indicate higher ethical values).

Marketing Managers	Marketing Research	Advertising
9	7	5
8	7	6
7	6	5
8	6	4
9	7	5
7	6	5

1. Compute the values identified below (to 1 decimal, if necessary).
   

   Sum of Squares, Treatment
   Sum of Squares, Error
   Mean Squares, Treatment
   Mean Squares, Error

   
   
2. Use = .05 to test for a significant difference in perception among the three groups.
   
   Calculate the value of the test statistic (to 2 decimals).
   
   
   The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10
   
   What is your conclusion?
   SelectConclude the mean perception scores for the three groups are not all the sameCannot conclude there are differences among the mean perception scores for the three groups
   
3. Using = .05, determine where differences between the mean perception scores occur.
   
   Calculate Fisher's LSD value (to 2 decimals).
   
   
   Test whether there is a significant difference between the means for marketing managers (1), marketing research specialists (2), and advertising specialists (3).
   

   Difference	Absolute Value	Conclusion
   1 - 2		SelectSignificant differenceNo significant difference
   1 - 3		SelectSignificant differenceNo significant difference
   2 - 3		SelectSignificant differenceNo significant difference

Answer 1

using minitab>stat>Anova>one way anova

we have

One-way ANOVA: Marketing Managers, Marketing Research, Advertising

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 3 Marketing Managers, Marketing Research, Advertising

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
treatment 2 27.000 13.5000 27.00 0.000
Error 15 7.500 0.5000
Total 17 34.500

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.707107 78.26% 75.36% 68.70%

Means

Factor N Mean StDev 95% CI
Marketing Managers 6 8.000 0.894 (7.385, 8.615)
Marketing Research 6 6.500 0.548 (5.885, 7.115)
Advertising 6 5.000 0.632 (4.385, 5.615)

Pooled StDev = 0.707107

Fisher Pairwise Comparisons

Grouping Information Using the Fisher LSD Method and 95% Confidence

Factor N Mean Grouping
Marketing Managers 6 8.000 A
Marketing Research 6 6.500 B
Advertising 6 5.000 C

Means that do not share a letter are significantly different.

Fisher Individual Tests for Differences of Means

Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value P-Value
Marketing Re - Marketing Ma -1.500 0.408 (-2.370, -0.630) -3.67 0.002
Advertising - Marketing Ma -3.000 0.408 (-3.870, -2.130) -7.35 0.000
Advertising - Marketing Re -1.500 0.408 (-2.370, -0.630) -3.67 0.002

Simultaneous confidence level = 88.31%

a )from output

Sum of Squares, Treatment	27.0
Sum of Squares, Error	7.5
Mean Squares, Treatment	13.5
Mean Squares, Error	0.5

b ) the value of the test statistic F=27.000

The p-value is0.000    which is less than .01

since p value is less than 0.01 so we reject Hi and conclude that  there are differences among the mean perception scores for the three groups

c)

Difference	Absolute Value	Conclusion
1 - 2	3.67	Significant difference
1 - 3	7.35	Significant difference
2 - 3	3.67	Significant difference