Question

An advertising company wants to know whether the size of an advertisement and the color of the advertisement make a difference in the response of magazine readers. A random sample of readers shown ads of 4 different colors and 3 different sizes. Assume that the ratings follow the normal distribution. The rating is shown in the following table:

Size of Ad	Color of Ad
	Red	Blue	Orange	Green
Small	4	3	3	8
Medium	3	5	6	7
Large	6	7	8	8

a. Using the Excel spreadsheet, construct an ANOVA table.

b. Is there a difference in the effectiveness of an advertisement by color at α =.05? (in your answer, you need to indicate F-static and critical value of F)

c.  Is there a difference in the effectiveness of an advertisement by size at α =.05 ? (in your answer, you need to indicate F-static and critical value of F)

Answer 1

Solution:-

a)

b)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃ = u₄

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 3.797

F_critical = 4.757

Interpret results. Since the F-value (3.797) does not lies in the rejection region, we failed to reject the null hypothesis.

Conclusion:-

Reject H₀, There is sufficient evidence for significant differences between the three kinds.

c)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃ = u₄

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 4.932

F_critical = 5.143

Interpret results. Since the F-value (4.932) does not lies in the rejection region, we failed to reject the null hypothesis.