Question

In the digital age of marketing, special care must be taken to make sure that programmatic ads appearing on websites align with a company's strategy, culture and ethics. For example, in 2017, Nordstrom, Amazon and Whole Foods each faced boycotts from social media users when automated ads for these companies showed up on the Breitbart website (ChiefMarketer.com). It is important for marketing professionals to understand a company's values and culture. 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
5	5	6
4	6	6
4	6	6
3	5	6
5	5	5
3	6	7

(a)

Use α = 0.05 to test for significant differences in perception among the three groups.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: μ_MM = μ_MR = μ_A

H₀: μ_MM = μ_MR = μ_A

H_a: Not all the population means are equal.   

H₀: μ_MM ≠ μ_MR ≠ μ_A
H_a: μ_MM = μ_MR = μ_A

H₀: μ_MM = μ_MR = μ_A
H_a: μ_MM ≠ μ_MR ≠ μ_A

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

Find the value of the test statistic.

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that the mean perception score is not the same for the three groups of specialists.

Reject H₀. There is sufficient evidence to conclude that the mean perception score is not the same for the three groups of specialists.   

Reject H₀. There is not sufficient evidence to conclude that the mean perception score is not the same for the three groups of specialists.

Do not reject H₀. There is not sufficient evidence to conclude that the mean perception score is not the same for the three groups of specialists.

(b)

At the α = 0.05 level of significance, we can conclude that there are differences in the perceptions for marketing managers, marketing research specialists, and advertising specialists. Use the procedures in Section 13.3 to determine where the differences occur. Use α = 0.05. (Use the Bonferroni adjustment.)

Find the value of LSD. (Round your comparison wise error rate to four decimal places. Round your answer to three decimal places.)

LSD =

Find the pairwise absolute difference between sample means for each pair of treatments.

[x_MM − x_{MR] =}

[x_MM − x_{A] =}

[x_MR − x_{A] =}

Where do the significant differences occur? (Select all that apply.)

There is a significant difference in the perception of corporate ethical values between marketing managers and marketing research specialists.

There is a significant difference in the perception of corporate ethical values between marketing managers and advertising specialists.

There is a significant difference in the perception of corporate ethical values between marketing research specialists and advertising specialists.

There are no significant differences.

Answer 1

Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array):

Source	SS	df	MS	F	P value
Between	13.00	2	6.500	13.000	0.0005
Within	7.50	15	0.5000
Total	20.50	17

a)

H₀: μ_MM = μ_MR = μ_A

H_a: Not all the population means are equal.   

value of the test statistic F =13.00

p value =0.001

Reject H₀. There is sufficient evidence to conclude that the mean perception score is not the same for the three groups of specialists.   

b)

Bonferroni crtiical value for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =

1.10

Difference	Absolute Value	Conclusion
x1-x2	1.50	significant difference
x3-x1	2.00	significant difference
x3-x2	0.50	not significant difference

There is a significant difference in the perception of corporate ethical values between marketing managers and marketing research specialists.

There is a significant difference in the perception of corporate ethical values between marketing managers and advertising specialists.