Answer:
d. No because n·(1 - ) = 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· > 10
c. Yes, because we know that the population is evenly distributed
d. No, because the n·(1 - ) 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, = 0.67
The number of women in the sample of women, n₂ = 56
The proportion of men who dislike anchovies, = 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· ≥ 10, and n·(1 -
) ≥ 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, n₁·₁ = 41 × 0.67 = 24.47 > 10
n₁·(1 - ₁) = 41 × (1 - 0.67) = 13.53 > 10
For the sample of women, n₂·₂ = 56 × 0.84 = 47.04 > 10
n₂·(1 - ₂) = 56 × (1 - 0.84) = 8.96 < 10
Therefore, the for n₂·(1 - ₂), the sample does not meet the requirement for normality
The correct option is d. No because n₂·(1 - ₂) = 8.96 is less than 10