A marketing research firm tests the effectiveness of three new flavorings for a

ID: 3310827 • Letter: A

Question

A marketing research firm tests the effectiveness of three new flavorings for a leading beverage using a sample of 30 people, divided randomly into three groups of 10 people each. Group 1 tastes flavor 1, group 2 tastes flavor 2 and group 3 tastes flavor 3. Each person is then given a questionnaire, which evaluates how enjoyable the beverage was. The scores are as in Figure 1. Determine whether there is a perceived significant difference between the three flavorings. Use a significance level of -035 2. Flavor 1 Flavor 3 Flavor 2 12 13 17 19 11 16 14 20 15 14 16 19 19 15 12 10 10 18 14 16 111

Explanation / Answer

Solution:

Here, we have to use one way analysis of variance or single factor ANOVA F test for checking the following null and alternative hypothesis:

Null hypothesis: H0: The average effectiveness for the given three flavours is same.

Alternative hypothesis: Ha: The average effectiveness for the given three flavours is not same.

H0: µ1 = µ2 = µ3 versus Ha: At least two means are not equal.

We are given a level of significance or alpha value 0.035.

Required ANOVA table for the given test is summarised as below:

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Flavor 1

150

13.33333

Flavor 2

111

11.1

18.76667

Flavor 3

135

13.5

14.05556

ANOVA

Source of Variation

P-value

F crit

Between Groups

77.4

38.7

2.515407

0.099596

3.354131

Within Groups

415.4

15.38519

Total

492.8

For the above ANOVA table, the test statistic value is given as F = 2.5154 and p-value for this test is given as 0.099596.

P-value = 0.099596 > = 0.035

We do not reject the null hypothesis that average effectiveness for the given three flavours is same.

There is sufficient evidence to conclude that average effectiveness for the given three flavours is same.