Question

The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals specializing in marketing (higher scores indicate higher ethical values).

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

1. [6] Use Minitab and α = 0.05 to test for significant differences in perception among the three groups. In the calculations section, insert only that portion of your output that is pertinent. Complete the components of the test.

[1] Hypothesis:         

[1] Decision rule:

    

[2] Calculations (insert only the portion of your Minitab output pertinent to this part):

[2] Conclusions:

2. [1] If you determined a significant difference in part a, use Minitab to conduct a Fisher’s LSD procedure to determine where the differences occur. Insert the pertinent output.

3. [3 – 1 for output; 2 for conclusions] Develop a boxplot (using Minitab). Use a single plot and put all three boxplots together. Use the plot and your results in part b to assess which group is the most ethical and which is the least. Plot (shrink down by using the handle on the bottom right

Answer 1

## 1 ) Use Minitab and α = 0.05 to test for significant differences in perception among the three groups. In the calculations section, insert only that portion of your output that is pertinent. Complete the components of the test.

Answer : we have given three treatment :

# Hypothesis: Ho : μ1 = μ2 = μ3 ( All treatment means are equal

vs

H1 : At least one treatment mean is differ

## Decision rule:

1 ) using critical value approach : we reject Ho if F statistics value is greater than F critical value ,

2 ) using p value approach : we reject Ho if p value is less than alpha value .

( from critical value and p value approach both give same result )

## Calculations (insert only the portion of your Minitab output pertinent to this part):

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
Factor 2 7.000 3.5000 7.00 0.007
Error 15 7.500 0.5000
Total 17 14.500

## here from anova : p value is less than alpha value we reject Ho

### Conclusions: There is sufficient evidence to conclude that at least one treatment mean is differ at given level of significance .

## b )  If you determined a significant difference in part a, use Minitab to conduct a Fisher’s LSD procedure to determine where the differences occur. Insert the pertinent output.

Answer : output of the fisher lsd :

Fisher Pairwise Comparisons

Grouping Information Using the Fisher LSD Method and 95% Confidence

Factor N   Mean   Grouping
Advertising 6 6.000 A
Marketing Managers   6 5.000 B
Marketing Research 6 4.500 B

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 -0.500 0.408 (-1.370, 0.370) -1.22 0.240
Advertising - Marketing Ma 1.000 0.408 ( 0.130, 1.870) 2.45 0.027
Advertising - Marketing Re 1.500 0.408 ( 0.630, 2.370) 3.67 0.002

Simultaneous confidence level = 88.31%

## Conclusion : if interval include null value we can say that it is not significant or there is no mean difference in pairs :

here for Marketing Re - Marketing Ma have interval include null value hence it is not significant and pair

Advertising - Marketing Ma , Advertising - Marketing Re not include null value hence it is significant .

##

Develop a boxplot (using Minitab). Use a single plot and put all three boxplots together. Use the plot and your results in part b to assess which group is the most ethical and which is the least. Plot (shrink down by using the handle on the bottom right

Answer : from plot we can say that advertising is most ethical than others two .