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). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire this year, 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. What is the value of the appropriate test statistic to test this claim? A) t₁₄₃ = 0.721 B) z = 0.721 C) t₁₄₃ = 1.96 D) z = 1.96

Question

Quizplus · Accepted Answer

The appropriate test statistic for this scenario is a z-score, which is calculated using the formula for a proportion test. Given that 72 out of 144 tasters preferred the competitor's blend, the sample proportion is 0.5. The null hypothesis proportion (p0) is 0.47, representing the proportion of consumers who preferred the competitor's blend before the recipe tweak. The standard error (SE) for the proportion is calculated using the formula SE = sqrt[p0(1-p0)/n], where n is the sample size. Plugging in the values, SE = sqrt[0.47(1-0.47)/144]. The z-score is then calculated as (p - p0)/SE, where p is the sample proportion. This calculation results in a z-score of approximately 0.721, making choice B the correct answer.

Vermont-Based Green Mountain Coffee Roasters Dominates the Market for Single-Serve