Exhibit 9-7.Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States,with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune,February 26,2011).But Keurig's patent on K-cups,the plastic pods used to brew the coffee,is expected to expire in 2012,allowing other companies to better compete.Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters.After tweaking its recipe,the competitor conducts a test with 144 tasters,of which 72 prefer its blend.The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. Refer to Exhibit 9-7.What is the value of the appropriate test statistic to test this claim?

Question

Quizplus · Accepted Answer

The appropriate test statistic in this scenario would be a z-test for proportions since we are comparing the proportion of consumers who prefer the competitor's blend to the proportion who prefer Green Mountain Coffee Roasters' French Roast. The test statistic can be calculated as (p - P) / sqrt[P * (1 - P) / n], where p is the sample proportion (0.5 in this case, since 72 out of 144 tasters preferred the new blend), P is the hypothesized proportion (0.47 in this case, since the competitor claims that their blend is preferred by more than 47% of consumers), and n is the sample size (144 in this case). Plugging in these values, we get a test statistic of approximately 2.16, which corresponds to choice B.