What is an important effect of the law of large numbers?

The law of large numbers is a fundamental principle in statistics that states that as the size of a sample increases, the sample mean will get closer to the expected value (or population mean). This means that if you take a large enough sample from a population, the average of your sample will tend to be very close to the true average of the population from which it is drawn.

This principle is crucial in many fields, including economics, risk assessment, and quality control, as it underscores the importance of large sample sizes when making inferences about a population based on sample data. A larger sample reduces the effect of random variation, making the estimate more reliable and accurate.

The other options do not accurately capture the essence of the law of large numbers. For instance, the idea that the average outcome remains the same regardless of sample size and that sample variability decreases as sample size decreases are not aligned with statistical principles. Additionally, the notion that prediction accuracy decreases with larger samples contradicts the basic premise of the law, which indicates that larger samples yield more reliable outcomes. Therefore, the correct understanding lies in the relationship of sample size to the accuracy of estimates, highlighting why larger samples approach the population average.