Business Degree Certification Practice Test

What happens to the shape of the sampling means as the sample size increases?

1. It cannot be predicted

2. It approaches a normal distribution

3. It becomes positively skewed

4. It becomes negatively skewed

The correct answer is: It approaches a normal distribution

As the sample size increases, the distribution of the sampling means approaches a normal distribution due to the Central Limit Theorem. This theorem states that regardless of the original distribution of the population from which samples are drawn, the distribution of the sample means will tend to resemble a normal distribution as the sample size becomes large, typically considered to be 30 or more. The reason for this tendency lies in the averaging process; as larger samples are taken, extreme values or outliers have less influence on the overall mean. Consequently, the variability among the means of various samples decreases, leading to a more concentrated group of means around the population mean, which manifests as a bell-shaped curve characteristic of normal distributions. Thus, the correct answer emphasizes the predictable behavior of sampling means in relation to sample size, reinforcing the fundamental principles of statistical inference. The other options, which suggest unpredictability or specific skewness, do not accurately reflect the established statistical understanding of how sample means behave in response to increasing sample size.