Question

2. Evaluate the following statement. To answer this question please state the Central Limit Theorem and explain why central limit theorem is so important. The samples mean of a random sample of n observations from a normal population with mean u and variance o2 is a sampling statistics. The sample mean is normally distributed with mean u and variance oʻ/n due to central limit theorem.

Answer 1

From the given information,

The given statement is nothing but statement of central limit theorem provided that sample size (n) is sufficiently large.

And central limit theorem is very important because this theorem allows you to simplify problems in statistics by allowing you to work with a distribution that is approximately normal.

Also

The central limit theorem tells us that no matter what the distribution of the population is, the shape of the sampling distribution will approach normality as the sample size (N) increases.

Thank you.