A local winery wants to create better marketing campaigns for its white wines by understanding its customers better. One of the general belief has been that higher proportion of women prefer white wine as compared to men. The company has conducted a research study in its local winery on white wine preference. Of a sample of 500 men, 120 preferred white wine and of a sample of 500 women, 210 preferred white wine. Using a 0.05 level of significance test this claim.

There is sufficient evidence in support of the claim that a higher proportion of women prefer white wine as compared to men

Step-by-step explanation:

In order to test the claim, we list out the given parameters as follows;

The number of men in the sample of men, n₁ = 500

The number of men in the sample of men, that prefer white wine x = 120

The number of women in the sample of women, n₂ = 500

The number of women in the sample of women, that prefer white wine x = 210

The significance level of the test, α = 0.05

The proportion of men that prefer white wine, p₁ = 210/500 = 0.42

The proportion of women that prefer white wine, p₂ = 120/500 = 0.24

S.E = 0.029

The null hypothesis, H₀: (p₁ - p₂) ≥ 0

The alternative hypothesis, Hₐ: p ≥ 0.42

The test statistic is given by the following formula;

∴ Z = (0.42 - 0.24)/0.029 ≈ 6.207

∴ The p-Value = 1

Given that the p-Value is larger than the significance level, therefore, there is significant evidence supporting the null hypothesis that there is a higher proportion of women who prefer white wine as compared to men

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