The sampling distribution of is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes n₁ and n₂ are large.

Question

Quizplus · Accepted Answer

The statement is correct. When the sample sizes are large (n₁ and n₂), the central limit theorem holds and the sampling distribution of the mean becomes approximately normal, even if the populations from which the samples were drawn are non-normal. However, if the sample sizes are small, or if there are outliers or skewness in the populations, the normality assumption may not hold.

The Sampling Distribution of Is Normal If the Sampled