In 2018, a consumer goods giant had more than 20 brands with more than $1 billion in annual sales. How does the company create so many successful consumer products? They effectively invests in research and development to understand what consumers want. One method used to determine consumer preferences is called conjoint analysis. Conjoint analysis allows a company to ascertain the utility that a respondent in the conjoint study places on a design of a given product. The higher the utility, the more valuable a respondent finds the design. Suppose we have conducted a conjoint stud and have the following estimated utilities (higher is preferred) for each of three different designs for a new whitening toothpaste. Respondent 1 2 3 4 5 6 7 8 9 10 Design A 24.6 31.4 31.8 15.4 20.7 41.0 27.1 20.2 31.6 24.4 Utilities Design B 34.4 31.4 20.2 26.4 18.3 34.0 22.5 21.8 29.4 29.0 Design C 28.8 33.9 27.8 25.1 18.2 44.8 27.3 27.9 31.3 29.3 At the 0.05 level of significance, test for any significant differences.
In 2018, a consumer goods giant had more than 20 brands with more than $1 billion in annual sales. How does the company create so many successful consumer products? They effectively invests in research and development to understand what consumers want. One method used to determine consumer preferences is called conjoint analysis. Conjoint analysis allows a company to ascertain the utility that a respondent in the conjoint study places on a design of a given product. The higher the utility, the more valuable a respondent finds the design. Suppose we have conducted a conjoint stud and have the following estimated utilities (higher is preferred) for each of three different designs for a new whitening toothpaste. Respondent 1 2 3 4 5 6 7 8 9 10 Design A 24.6 31.4 31.8 15.4 20.7 41.0 27.1 20.2 31.6 24.4 Utilities Design B 34.4 31.4 20.2 26.4 18.3 34.0 22.5 21.8 29.4 29.0 Design C 28.8 33.9 27.8 25.1 18.2 44.8 27.3 27.9 31.3 29.3 At the 0.05 level of significance, test for any significant differences.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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Transcribed Image Text:At the 0.05 level of significance, test for any significant differences.
State the null and alternative hypotheses.
O Ho: Not all the population means are equal.
Ha: Design A
O Ho: MDesign A
Ho:
: At least two of the population means are equal.
Ha: At least two of the population means are different.
Ha: Design A
Ho: MDesign A
=
#
Ha: Design A
=
=
=
MDesign B Design C
#
MDesign B
MDesign B
#
=
=
MDesign B
Design B +
Design B
Design C
=
O Ho: MDesign A
Design C
Ha: Not all the population means are equal.
Find the value of the test statistic. (Round your answer to two decimal places.)
Design C
Design C
Design C
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
Do not reject Ho. There is not sufficient evidence to conclude that there is a difference in design.
Reject Ho. There is sufficient evidence to conclude that there is a difference in design.
Reject Ho. There is not sufficient evidence to conclude that there is a difference in design.
Do not reject Ho. There is sufficient evidence to conclude that there is a difference in design.
Transcribed Image Text:In 2018, a consumer goods giant had more than 20 brands with more than $1 billion in annual sales. How does the company create so many successful consumer products? They effectively invests in
research and development to understand what consumers want. One method used to determine consumer preferences is called conjoint analysis. Conjoint analysis allows a company to ascertain the
utility that a respondent in the conjoint study places on a design of a given product. The higher the utility, the more valuable a respondent finds the design. Suppose we have conducted a conjoint study
and have the following estimated utilities (higher is preferred) for each of three different designs for a new whitening toothpaste.
Respondent
1
2
3
4
5
6
7
8
9
10
Design A
24.6
31.4
31.8
15.4
20.7
41.0
27.1
20.2
31.6
24.4
Utilities
Design B
34.4
31.4
20.2
26.4
18.3
34.0
22.5
21.8
29.4
29.0
Design C
28.8
33.9
27.8
25.1
18.2
44.8
27.3
27.9
31.3
29.3
At the 0.05 level of significance, test for any significant differences.
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