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. Utilities Respondent Design A Design B Design C 1 24.6 34.4 28.8 2 31.4 31.4 33.9 3 31. 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. State the null and alternative hypotheses. O Ho: HDesign A # H Design B # Design C Hai Design A = /Design B = /Design C O Ho: At least two of the population means are equal. Ha: At least two of the population means are different. O Ho: HDesign A = Design B = H Design C Hai Design A * Design B = /Design C O Ho: HDesign A = HDesign B = /Design C H: Not all the population means are equal. O Ho: Not all the population means are equal. Ha: HDesign A = /Design B = /Design CFind the value of the test statistic. (Round your answer to two decimal places.) 0.53 x Find the p-Value. [Round your answer to three decimal places.) o-value = [1.596 x State your conclusion. a?) Do not reject H0. There is not sufcient evidence to conclude that there is a difference in design. '._:- Do not reject H0. There is sufficient evidence to conclude that there is a difference in design. -\\. '._,- Reject H0. There is sufficient evidence to conclude that there is a difference in design. Pi '._,- Reject H0. There is not sufficient evidence to conclude that there is a difference in design