With large samples and a small population variance, the sample means usually
A) will be close to the population mean.
B) will slightly underestimate the population mean.
C) will slightly overestimate the population mean.
D) will equal the population mean.

Question

Quizplus · Accepted Answer

With large samples (due to the central limit theorem) and a small population variance, the sample means will be close to the population mean. This is because the distribution of sample means will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, the majority of sample means will fall within a few standard deviations of the population mean, resulting in the sample means being close to the population mean.

With Large Samples and a Small Population Variance, the Sample