According to the central limit theorem,
A) The population mean and the mean of all sample means are equal.
B) Increasing sample size decreases the dispersion of the sampling distribution.
C) The sampling distribution of the sample means is approximately normally distributed.
D) The sampling distribution of the sample means will be skewed.

Question

Quizplus · Accepted Answer

The central limit theorem states that as sample size increases, the sampling distribution of the sample means will tend towards a normal distribution regardless of the distribution of the population from which the samples are taken. Therefore, C is the correct answer. A is false because the population mean and mean of sample means are not necessarily equal. B is false because increasing sample size may decrease variability, but it does not necessarily decrease dispersion. D is false because the central limit theorem applies to normal distributions as well as non-normal distributions, so the sampling distribution of the sample means is not necessarily skewed.

According to the Central Limit Theorem