Question

Graeter’s is thinking about expanding its ice cream flavors. They have created three new flavors of ice cream: (1) Lemon Merengue Pie, (2) Butterscotch, and (3) Banana Cream Pie. They recruit 18 people to participate in their study, and they assign each participant to taste-test one of their new ice cream flavors. After tasting the flavor, participants rate their likelihood of ordering that ice cream flavor on their next trip to Graeter’s, using a scale from 1 (I definitely wouldn’t order this flavor) to 10 (I definitely would order this flavor). The data is as follows:

Participant	Ice Cream Flavor	Ice Cream Rating
1	Lemon Merengue Pie	7
2	Lemon Merengue Pie	6
3	Lemon Merengue Pie	8
4	Lemon Merengue Pie	5
5	Lemon Merengue Pie	7
6	Lemon Merengue Pie	9
7	Butterscotch	4
8	Butterscotch	5
9	Butterscotch	3
10	Butterscotch	1
11	Butterscotch	6
12	Butterscotch	2
13	Banana Cream Pie	7
14	Banana Cream Pie	8
15	Banana Cream Pie	6
16	Banana Cream Pie	10
17	Banana Cream Pie	9
18	Banana Cream Pie	8

For this problem, complete the following steps. You must show ALL OF YOUR WORK to receive credit for this problem.(21 pts.)

(1) Identify the two hypotheses. (2 pts.)

(2) Determine the critical region for your decision (use α = 0.05). (3 pts.)

(3) Compute the test statistic. (8 pts.)

(4) Use the test statistic to make a decision and interpret that decision. (1 pt.)

(5) If needed, conduct a post hoc test. (5 pts.)

(6) Compute and interpret η2 as a measure of the effect size.(2 pts.)

Answer 1

1) Null Hypothesis: The means of the three groups are equal that is

Alternate Hypothesis: The means of all the groups are not equal that is

2) Critical Region: We shall reject the null hypothesis at level iff

where is the upper , otherwise we accept it .

3) First we will arrange the observation in table form and then conduct one way ANOVA

Lemon merengue pie	Butterscotch	Banana cream pie
7	4	7
6	5	8
8	3	6
5	1	10
7	6	9
9	2	8

Let the different flavours of ice cream be denoted by factor A

Sum of squares due to factor A (SSA)= 67

DF= 3-1=2

MSA= 33.5

Total sum of squares (TSS) = 104.5

Total DF = 18-1 = 17

Sum of squares due to error = TSS-SSA = 37.50

DF = 17-2 = 15

MSE= 2.5

Test Statistic : Obs F = MSA/MSE= 13.40

4)   

That is we reject the null Hypothesis .