Question

Consider two population distributions labeled X and Y. Distribution X is highly skewed while the distribution Y is slightly skewed. In order for the sampling distributions of X and Y to achieve the same degree of normality

A. Population Y will require a larger sample size
B. Population X will require a larger sample size
C. Population X and Y will require the same sample size
D. None of the above

Answer 1

Answer: B. Population X will require a larger sample size

Explanation:

• If a random variable say p has skewed distribution (whether right or left ) in a population then a bigger sample size is needed to make sure that the sampling distribution follows normal distribution.

Given : Two population distributions labeled X and Y.

Distribution X → highly skewed

Distribution Y → slightly skewed.

Since Distribution X more skewed so , we will need a larger sample size of population X as compared to Y.

Hence, the correct answer is B. Population X will require a larger sample size