Question

In: Statistics and Probability

There are three types of ice cream: soft serve, hard packed, and frozen yogurt. An experiment...

There are three types of ice cream: soft serve, hard packed, and frozen yogurt. An experiment was performed to compare these three types of ice cream with customers. The other factors included were age, adolescents and teenagers. As well as flavors: vanilla, chocolate, mixed. Carry out a test using a significance level of 10%.

  1. Provided the data, what are the significance of the factors of ice cream? Include differences which exist within the significant effects.
  2. Develop a linear model predicting the test result.
  3. What is the test result of an adolescent who wants a Mixed flavor of Hard Packed ice cream?
Soft Serve Hard Packed Frozen Yogurt
Vanilla Chocolate Mixed Vanilla Chocolate Mixed Vanilla Chocolate Mixed
10 12 10 15 12 6 13 11 10
Adolescents 12 9 11 12 10 7 9 7 6
13 10 9 14 11 5 11 8 8
16 11 12 17 14 10 16 10 11
Teenagers 14 13 11 18 13 9 12 12 10
17 15 13 16 12 11 14 14 9

Solutions

Expert Solution

1. The ANOVA table is:

Source DF Adj SS Adj MS F-Value P-Value
Age 1 115.574 115.574 51.84 0.000
Type of Ice Cream 2 22.333 11.167 5.01 0.011
Flavors 2 183.000 91.500 41.04 0.000
Age*Type of Ice Cream 2 0.259 0.130 0.06 0.944
Age*Flavors 2 1.815 0.907 0.41 0.668
Type of Ice Cream*Flavors 4 39.333 9.833 4.41 0.005
Error 40 89.185 2.230
Lack-of-Fit 4 5.852 1.463 0.63 0.643
Pure Error 36 83.333 2.315
Total 53 451.500

There is a significant main effect of Age.

There is a significant main effect of Type of Ice Cream.

There is a significant main effect of Flavors.

There is a significant interaction effect of Type of Ice Cream and Flavors.

2. The linear model is:

y = 11.500 - 1.463 Age_Adolescents + 1.463 Age_Teenagers - 0.889 Type of Ice Cream_Frozen
Yogurt + 0.278 Type of Ice Cream_Hard Packed + 0.611 Type of Ice Cream_Soft Serve
- 0.167 Flavors_Chocolate - 2.167 Flavors_Mixed + 2.333 Flavors_Vanilla
+ 0.074 Age*Type of Ice Cream_Adolescents Frozen Yogurt
- 0.093 Age*Type of Ice Cream_Adolescents Hard Packed
+ 0.019 Age*Type of Ice Cream_Adolescents Soft Serve
- 0.074 Age*Type of Ice Cream_Teenagers Frozen Yogurt
+ 0.093 Age*Type of Ice Cream_Teenagers Hard Packed
- 0.019 Age*Type of Ice Cream_Teenagers Soft Serve + 0.130 Age*Flavors_Adolescents
Chocolate + 0.130 Age*Flavors_Adolescents Mixed - 0.259 Age*Flavors_Adolescents Vanilla
- 0.130 Age*Flavors_Teenagers Chocolate - 0.130 Age*Flavors_Teenagers Mixed
+ 0.259 Age*Flavors_Teenagers Vanilla - 0.111 Type of Ice Cream*Flavors_Frozen Yogurt
Chocolate + 0.556 Type of Ice Cream*Flavors_Frozen Yogurt Mixed
- 0.444 Type of Ice Cream*Flavors_Frozen Yogurt Vanilla
+ 0.389 Type of Ice Cream*Flavors_Hard Packed Chocolate
- 1.611 Type of Ice Cream*Flavors_Hard Packed Mixed
+ 1.222 Type of Ice Cream*Flavors_Hard Packed Vanilla
- 0.278 Type of Ice Cream*Flavors_Soft Serve Chocolate
+ 1.056 Type of Ice Cream*Flavors_Soft Serve Mixed
- 0.778 Type of Ice Cream*Flavors_Soft Serve Vanilla

3. There is a main effect of an adolescent who wants a Mixed flavor of Hard Packed ice cream.

The data is:

Age Type of Ice Cream Flavors
Adolescents Soft Serve Vanilla 10
Adolescents Soft Serve Vanilla 12
Adolescents Soft Serve Vanilla 13
Teenagers Soft Serve Vanilla 16
Teenagers Soft Serve Vanilla 14
Teenagers Soft Serve Vanilla 17
Adolescents Soft Serve Chocolate 12
Adolescents Soft Serve Chocolate 9
Adolescents Soft Serve Chocolate 10
Teenagers Soft Serve Chocolate 11
Teenagers Soft Serve Chocolate 13
Teenagers Soft Serve Chocolate 15
Adolescents Soft Serve Mixed 10
Adolescents Soft Serve Mixed 11
Adolescents Soft Serve Mixed 9
Teenagers Soft Serve Mixed 12
Teenagers Soft Serve Mixed 11
Teenagers Soft Serve Mixed 13
Adolescents Hard Packed Vanilla 15
Adolescents Hard Packed Vanilla 12
Adolescents Hard Packed Vanilla 14
Teenagers Hard Packed Vanilla 17
Teenagers Hard Packed Vanilla 18
Teenagers Hard Packed Vanilla 16
Adolescents Hard Packed Chocolate 12
Adolescents Hard Packed Chocolate 10
Adolescents Hard Packed Chocolate 11
Teenagers Hard Packed Chocolate 14
Teenagers Hard Packed Chocolate 13
Teenagers Hard Packed Chocolate 12
Adolescents Hard Packed Mixed 6
Adolescents Hard Packed Mixed 7
Adolescents Hard Packed Mixed 5
Teenagers Hard Packed Mixed 10
Teenagers Hard Packed Mixed 9
Teenagers Hard Packed Mixed 11
Adolescents Frozen Yogurt Vanilla 13
Adolescents Frozen Yogurt Vanilla 9
Adolescents Frozen Yogurt Vanilla 11
Teenagers Frozen Yogurt Vanilla 16
Teenagers Frozen Yogurt Vanilla 12
Teenagers Frozen Yogurt Vanilla 14
Adolescents Frozen Yogurt Chocolate 11
Adolescents Frozen Yogurt Chocolate 7
Adolescents Frozen Yogurt Chocolate 8
Teenagers Frozen Yogurt Chocolate 10
Teenagers Frozen Yogurt Chocolate 12
Teenagers Frozen Yogurt Chocolate 14
Adolescents Frozen Yogurt Mixed 10
Adolescents Frozen Yogurt Mixed 6
Adolescents Frozen Yogurt Mixed 8
Teenagers Frozen Yogurt Mixed 11
Teenagers Frozen Yogurt Mixed 10
Teenagers Frozen Yogurt Mixed 9

orchestra answered 1 year ago
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