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In order to plan a new advertising campaign, a marketing firm wants to know whether men in a certain area of the country are more likely to purchase a convertible than women in that same area. To gather data, they took a random sample of men and a random sample of women who had recently purchased a new vehicle and then determined both the proportion of men and the proportion of women who had purchased a convertible. A $90\%$ confidence interval for the difference in the proportion of men vs. women who purchased a convertible was found to be $(-0.021, 0.115)$.

Based on this confidence interval should the marketing firm conclude that the proportion of men who purchase a convertible is higher than the proportion of women who purchase a convertible?

A

Yes. Most of the confidence interval consists of positive values which show that the proportion of men who purchase a convertible is greater than the proportion of women who purchase a convertible.

B

Yes. The proportion of women who purchase a convertible was estimated to be $0.021$ while the proportion of men who purchase a convertible was estimated to be $0.115$.

C

Yes. The difference in proportions of men and women who purchased a convertible was $0.047$ and this value is well above $0$.

D

No. Since $0$ is included in the confidence interval, there may be no difference in the proportion of men and the proportion of women who purchase a convertible.

E

No. The proportion of men who purchase a convertible was estimated to be $0.021$ while the proportion of women who purchase a convertible was estimated to be $0.115$. It actually appears that the proportion of women who purchase a convertible is higher than the proportion of men who purchase a convertible.

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