Question

A researcher is interested in the effects of product placements on brand attitudes. The researcher randomly assigns 15 students to watch a short film that includes negative product placements, no product placements, or positive product placements for Starbucks. The researcher then assesses attitudes toward the Starbucks brand (1 = dislike very much to 7 = like very much). The data are shown below. Conduct a one-way ANOVA by hand. State the null and alternative. Identify the F-critical value. Compute the F-obtained. And determine whether placement type has an impact on brand attitudes. Use alpha = .05.

Data:

Negative: 2 1 2 1 4

No Placement: 4 5 3 3 5

Positive: 6 4 4 5 6

Step 1: Establish null and alternate hypotheses

Step 2: Calculate the degrees of freedom

Step 3: Calculate F critical using critical F– table

Step 4: Calculate the Sum of Square deviation (SSD)

Step 5: Calculate F obtained

Step 6: Specify the critical value and the obtained value on a f-distribution curve + ANOVA table

Step 7: Decision and Conclusion

Answer 1

Solution:-

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

Null hypothesis: u₁ = u₂ = u₃

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.

2)

DF_between = 2

DF_treatments = 12

3)

F_critical = 3.885

Rejection region is F > 3.885

5)

F statistics is given by:-

$F=\frac{MSB}{MSE}$

F = 10.0

Interpret results. Since the F-value (10) is lies in the critical region, we have to reject the null hypothesis.

Conclusion:-

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