Central Limit Theorem and The Law of Large Numbers

Question

Explain the Central Limit Theorem and the Law of Large Numbers. There are 3 key points. Include the formula for the standard error.

Answer 1

The Central Limit Theorem refers to the fact that the distribution of sample means shows a normal distribution as the sample size increases. So, if the sample size is greater than or equal to 30, then the shape of the distribution is normal. The Central Limit theorem is often used as a way to verify the conditions for a significance test.

The Law of Large Numbers is similar to the central limit theorem in that it is used to verify if the distribution of the data is normal. The difference is that the law of large numbers is used for confidence intervals instead of significance tests. For large numbers, if n(p)≥10, or n(1-p) ≥ 10, where p is the probability of the desired outcome, then the distribution is normal.

The formula for standard error is σ / √ (n)