A researcher is considering drawing a sample of size n from a negatively skewed parent population with a mean,$ \underline{u}$, and variance $\sigma$²; he should realize that n is ___, the sample mean x is ___ distributed with mean x and variance $\sigma$²/n (assuming the sample represents a small proportion of the population). A) small; normally B) large; normally C) small; binominally D) large; binominally E) none of the above

Question

Quizplus · Accepted Answer

For large sample sizes, the Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the parent population. This holds true even for negatively skewed populations. The mean of the sampling distribution of the sample mean is the same as the population mean, and the variance of the sampling distribution of the sample mean is the population variance divided by the sample size (n).

A Researcher Is Considering Drawing a Sample of Size N u‾ \underline{u}u​

A Researcher Is Considering Drawing a Sample of Size N $\underline{u}$