A study is planned to compare the proportion of men who dislike anchovies with t

Question

A study is planned to compare the proportion of men who dislike anchovies with the proportion of women who dislike anchovies. The study seeks to determine if the proportions of men and women who dislike anchovies are different. A sample of 41 men was taken and the p estimate for the true proportion of men who dislike anchovies was determined to be 0.67. A sample of 56 women was also taken and the p estimate for the true proportion of women who dislike anchovies was determined to be 0.84. Are the requirements satisfied to perform this hypothesis test? Why?

Question options:

A. Yes, because the sample sizes of both groups are greater than 5.

B. Yes, because in both cases np >10.

C. Yes, because we know that the populations are normally distributed.

D. No, because in at least one case n(1p )<10.

B. WAS INCORRECT

Explanation / Answer

If we consider the samples of women, then:

n(1 - p) = 56*(1 - 0.84) = 56*0.16 = 8.96 < 10

Hence,

The requirement is not being satisfied.

Option D is correct.

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