The central limit theorem asserts that as sample size increases:
A) the standard error increases.
B) the distribution of means becomes more normal.
C) the means become more dispersed with greater variability.
D) our confidence in the results decreases.

Question

Quizplus · Accepted Answer

The central limit theorem states that as sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, option B is correct. The standard error actually decreases with increasing sample size, so option A is incorrect. The means do not become more dispersed and variable with increasing sample size, so option C is also incorrect. Confidence in the results may actually increase with increasing sample size, so option D is incorrect.

The Central Limit Theorem Asserts That as Sample Size Increases