A market research firm is testing consumer reaction to a new shampod among age g

Question

A market research firm is testing consumer reaction to a new shampod among age groups in four regions. There are five consumers in each test panel. Each consumer completes a 10-question product satisfaction instrument with a 5 point scale (five is the highest rating) and the average score is recorded. Generate the appropriate outputs and perform the appropriate statistical tests to answer the questions below. Southeast Midwest We Youth 3.9 4.0 3.7 4.1 4.3 4.0 4.0 3.7 3.8 3.8 3.2 3.8 3.7 3.4 3.9 4.2 4.4 4.1 4.0 3.8 3.7 3.7 3.6 3.7 3.5 3.3 3.4 3.5 3.4 3.6 3.4 3.6 3.6 3.4 3.6 3.9 3.9 4.4 3.9 4.O 3.74.1 3.3 3.9 3.6 3.8 4.1 3.8 3.8 3.6 3.9 3.6 4.0 4.1 3.5 3.8 3.8 3.6 3.8 3.4 4.0 3.7 3.7 3.1 3.3 3.4 3.3 3.2 3.1 3.5 3.1 3.3 13.4 3.4 2.9 3.6 3.7 3.5

Explanation / Answer

ANOVA

TABLE

=

0.05

Row represents Regions and column represents Age Group

Source

DF

SS

MS

Fcal

Fcrit

Row

3

0.0625

0.0208

0.5510

2.7482

Column

3

4.1925

1.3975

36.9587

2.7482

Interaction

9

1.2445

0.1383

3.6569

2.0298

Between

15

5.4995

0.3666

Error

64

2.42

0.0378

Total

79

7.9195

0.1003

Conclusion

Since Fcal > Fcrit for column (Age group) and Interaction, only these two are significant.

=> there is enough evidence to suggest that average rating is different for different age groups and age group – region interaction has an impact on the rating. But, there is no difference in the average rating among regions.  

Now, ANSWERS part-wise

Region-wise difference in average rating: Answer NO

Region with lowest average rating: Answer NONE

Region with highst average rating: Answer NONE

Interaction between region and age group: Answer Yes

Age group having highest rating in South-east Region: Youth

DONE

ANOVA

TABLE

=

0.05

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