In a market research study conducted by a local winery on white wine preference,the following results were found.Of a sample of 500 men,120 preferred white wine and of a sample of 500 women,210 preferred white wine.Setup the alternative hypothesis that will test the claim that the percentage of women preferring white wine is 25% higher than men. A)P_w - P_m $\neq$ .25 B)P_w - P_m .25 C)P_w - P_m

Question

In a market research study conducted by a local winery on white wine preference,the following results were found.Of a sample of 500 men,120 preferred white wine and of a sample of 500 women,210 preferred white wine.Setup the alternative hypothesis that will test the claim that the percentage of women preferring white wine is 25% higher than men. A)P_w - P_m $\neq$ .25 B)P_w - P_m > .25 C)P_w - P_m < .25 D)P_w - P_m $\neq$ 0

Quizplus · Accepted Answer

The alternative hypothesis should state that the percentage of women preferring white wine is higher than the percentage of men by a certain amount. Option B states this directly by stating that the difference in proportions (P_w - P_m) is greater than 0.25. Since we are testing if the proportion for women is higher than men, we want a one-tailed test (greater than). Option A is incorrect as it includes the not-equal sign, which suggests a two-tailed test. Option C is also incorrect as it suggests testing if the proportion difference is less than 0.25, which is not what we are interested in. Option D is incorrect as it suggests testing if the proportion difference is exactly 0, which is not what the claim is about.

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