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.

1

24.6

34.4

28.8

2

31.4

31.4

33.9

3

31.8

20.2

27.8

4

15.4

26.4

25.1

5

20.7

18.3

18.2

6

41.0

34.0

44.8

7

27.1

22.5

27.3

8

20.2

21.8

27.9

9

31.6

29.4

31.3

10

24.4

29.0

29.3

At the 0.05 level of significance, test for any significant differences.

1. Find the value of the test statistic. (Round your answer to two decimal places.)

________

2. Find thep-value. (Round your answer to three decimal places.)

p-value = ________