Business Degree Certification Practice Test

According to the central limit theorem, how does sample size affect sampling error?

1. Directly related to the sample size, leading to larger sampling error

2. Inversely related to the sample size, making smaller sampling error with larger size

3. Directly correlated with population mean, increasing error with higher means

4. Inversely associated with population standard deviation, allowing larger error with smaller deviation

The correct answer is: Inversely related to the sample size, making smaller sampling error with larger size

The central limit theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. One of the key implications of this theorem is the relationship between sample size and sampling error. When the sample size increases, the variability of the sample means decreases. This reduction in variability results in a smaller standard error of the mean, which represents the average amount that sample means deviate from the true population mean. A larger sample size provides more information about the population and tends to yield more accurate estimates of population parameters, hence reducing sampling error. This relationship is crucial for statistical analysis and helps inform practices such as survey design and quality control, where ensuring accurate representation is vital. The smaller sampling error with larger sample sizes enables researchers to have greater confidence in their estimates, facilitating better decision-making based on statistical data.