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

Question

Mathematics

Andreas Vasquez

7 April, 23:13

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

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Answers (1)

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Cuddles · Answer 1

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

Step-by-step 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