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Andreas93 [3]
2 years ago
6

a study is planned to compare the proportion of men who dislike anchovies with the proportion of women who dislike anchovies. th

e 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
Mathematics
1 answer:
e-lub [12.9K]2 years ago
3 0

Answer:

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

Step-by-step 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 p₁  = 41 × 0.67 = 24.47 > 10

n₁·(1 - \hat p₁) = 41 × (1 - 0.67) = 13.53 > 10

For the sample of women, n₂·\hat p₂  = 56 × 0.84 = 47.04 > 10

n₂·(1 - \hat p₂) = 56 × (1 - 0.84) = 8.96 < 10

Therefore, the for n₂·(1 - \hat p₂), the sample does not meet the requirement for normality

The correct option is d. No because n₂·(1 - \hat p₂) = 8.96 is less than 10

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Step-by-step explanation:

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