Question

Consider two population distributions labeled A and B. Distribution A is highly skewed and nonnormal, while distribution B is slightly skewed and near normal. In order for the sampling distributions of A and B to achieve the same degree of normality: A. Population A will require a larger sample size. B. Population B will require a larger sample size. C. Populations A and B will require the same sample size. D. None of these.

Answer 1

A. Population A will require a larger sample size.

Explanation:

A highly skewed distribution shows that too much data is concentrated where it is highly skewed.

If the sample size in increased the data may not concentrate at the same point and the skewness is normal that is it is mesokurtic.

The normal curve called the mesokurtic is neither very peaked nor very flat topped.

Populations A and B cannot have the same sample size as there is difference in their skewness.

Therefore option C and D are incorrect.

Option B is also incorrect because if B will require a larger sample size then the skewness may almost finish and the data may have the same concentration at all points.It will become flat topped i.e platy kurtic.

So only option A is correct.

In creasing the sample size will make the curve normal and mesokurtic.