Question

Although after many trials proportions do tend to even out, this does not extend to small samples. This describes the:

a) Law of Large Numbers
b) Regression to the Mean
c) Central Limit Theorem
d) Law of Averages

Answer 1

The statement in the question is describing the Law of Large Numbers, which says that as the number of trials increases, the sample mean approaches the population mean, especially in large samples.

Step-by-step explanation:

The concept described in your question refers to the Law of Large Numbers, which states that as the number of trials in a probability experiment increases, the sample mean will tend to get closer and closer to the population mean. This law highlights that proportions in large samples are more likely to reflect the true population parameters, but this does not necessarily hold for small samples. The Central Limit Theorem (CLT) complements this by indicating that as the sample size grows, the distribution of the sample means becomes normal, with a mean that equals the population mean and a standard deviation that decreases with an increasing sample size. However, the Law of Large Numbers is the one that specifically addresses the relationship between trials proportions and how they even out over many trials.