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.Calculate the test statistic for testing the claim that women are 25% higher than men on preference for white wine.
A)6.167
B)-82.16
C)-2.397
D)-.07

Question

Quizplus · Accepted Answer

First, we need to calculate the proportion of men and women who prefer white wine:
Proportion of men who prefer white wine = 120/500 = 0.24
Proportion of women who prefer white wine = 210/500 = 0.42

Next, we need to calculate the expected proportion of women who prefer white wine if they were only 25% higher than men:
Expected proportion of women = 0.24 + 0.24(0.25) = 0.30

Now we can calculate the test statistic z:
z = (0.42 - 0.30) / sqrt((0.24)(0.76)/500 + (0.24)(0.01)/500) = 2.397

Using a significance level of 0.05 and a two-tailed test, the critical value of z is ±1.96. Since our calculated z value of 2.397 is greater than the critical value, we can reject the null hypothesis and conclude that women have a significantly higher preference for white wine than men.

In a Market Research Study Conducted by a Local Winery