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 approaches a normal distribution regardless of the underlying distribution of the population. Therefore, option C is the correct choice. Option A is incorrect because the population mean and sample means may not always be the same. Option B is incorrect because increasing sample size can decrease sampling variation, but not necessarily dispersion. Option D is incorrect because the central limit theorem assumes normality of the sampling distribution.

According to the Central Limit Theorem,________