# A common application of the sign test deals with analyzing consumer preferences. For instance, suppose that a

## Question:

The null hypothesis in this application says that there is no difference in preferences for Coke and Pepsi. If this null hypothesis is true, then the number of + 1 values in the population of all preferences should equal the number of - 1 values, which implies that the median preference Md = 0 (and that the proportion p of + 1 values equals .5). The alternative hypothesis says that there is a significant difference in preferences (or that there is a significant difference in the number of +1 values and - 1 values in the population of all preferences). This implies that the median preference does not equal 0 (and that the proportion p of + 1 values does not equal .5).

a. Table 18.1 gives the results of the taste test administered to the nine randomly selected consumers. If we consider testing H0: Md = 0 versus Ha: Md ≠ 0 where Md is the median of the (+1 and - 1) preference rankings, determine the values of S1, S2, and S for the sign test needed to test H0 versus Ha. Identify the value of S on the Excel add-in (MegaStat) output,

b. Use the value of S to find the p-value for testing H0: Md = 0 versus Ha: Md ≠ 0. Then use the p-value to test H0 versus Ha by setting a equal to .10, .05, .01, and .001. How much evidence is there of a difference in the preferences for Coke and Pepsi? What do you conclude?

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**Related Book For**

## Business Statistics In Practice

**ISBN:** 9780073401836

6th Edition

**Authors:** Bruce Bowerman, Richard O'Connell