Graeter’s is thinking about ex

 

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 for this problem.

  1. Identify the two hypotheses. 
  2. Determine the critical region for your decision (use α = 0.05). 
  3. Compute the test statistic. 
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Graeter’s is thinking about ex

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.

  1. Identify the two hypotheses.  
  2. Determine the critical region for your decision (use α = 0.05). 
  3. Compute the test statistic. 
  4. Use the test statistic to make a decision and interpret that decision. 
  5. If needed, conduct a post hoc test. 
  6. Compute and interpret η2 as a measure of the effect size.

Graeter’s is thinking about ex

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 Meringue Pie

7

2

Lemon Meringue Pie

6

3

Lemon Meringue Pie

8

4

Lemon Meringue Pie

5

5

Lemon Meringue Pie

7

6

Lemon Meringue 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

 

A) Identify the two hypotheses. 

B) Determine the critical region for your decision (use α = 0.05).

C) Compute the test statistic.

D) Use the test statistic to make a decision and interpret that decision. 

E) If needed, conduct a post hoc test. 

F) Compute and interpret η2 as a measure of the effect size. 

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