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

Answer 1

d. No because n·(1 -
`\hat p`) = 8.96 is less than 10

Explanation:

Question options;

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

b. Yes, because in both cases n·
`\hat p` > 10

c. Yes, because we know that the population is evenly distributed

d. No, because the n·(1 -
`\hat p`) is less than 10

Explanation;

The given data are;

The number of men in the sample of men, n₁ = 41

The proportion of men who dislike anchovies,
`\hat p_1` = 0.67

The number of women in the sample of women, n₂ = 56

The proportion of men who dislike anchovies,
`\hat p_2` = 0.84

The assumptions for an analysis of the difference between means using a T-test are;

1) The data should be from a random sample of the population

2) The variables should be approximately normal (n·
`\hat p` ≥ 10, and n·(1 -
`\hat p`) ≥ 10)

3) The scale of the data is a continuous ordinance scale

4) The sample size should be large

5) The sample standard deviations should be approximately equal

From the requirement for normality, we have;

For the sample of men, n₁·
`\hat p`₁ = 41 × 0.67 = 24.47 > 10

n₁·(1 -
`\hat p`₁) = 41 × (1 - 0.67) = 13.53 > 10

For the sample of women, n₂·
`\hat p`₂ = 56 × 0.84 = 47.04 > 10

n₂·(1 -
`\hat p`₂) = 56 × (1 - 0.84) = 8.96 < 10

Therefore, the for n₂·(1 -
`\hat p`₂), the sample does not meet the requirement for normality

The correct option is d. No because n₂·(1 -
`\hat p`₂) = 8.96 is less than 10