Graeter’s is thinking about expanding its ice cream flavors.They have created three new flavors of ice cream: (1) LemonMerengue Pie, (2) Butterscotch, and (3) Banana Cream Pie. Theyrecruit 18 people to participate in their study, and they assigneach participant to taste-test one of their new ice cream flavors.After tasting the flavor, participants rate their likelihood ofordering that ice cream flavor on their next trip to Graeter’s,using a scale from 1 (I definitely wouldn’t order this flavor) to10 (I definitely would order this flavor). The data is asfollows:
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 showALL 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 thatdecision. (1 pt.)
(5) If needed, conduct a post hoc test. (5 pts.)
(6) Compute and interpret η2 as a measure of the effect size.(2pts.)
