Which of the following can we conclude if we assume that the Central Limit Theorem is true?
A) The mean of the observed sample will always equal the mean of the population.
B) The variability of the observed sample will always equal the variability of the population.
C) The mean of the sampling distribution of means will always equal the population mean.
D) The variability of the sampling distribution of means will always equal the variability of the population.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of means will approach a normal distribution with a mean equal to the population mean, as the sample size increases. Therefore, we can conclude that the mean of the sampling distribution of means will always equal the population mean, if we assume the Central Limit Theorem is true. Option A is incorrect, as the mean of the observed sample may or may not be equal to the population mean. Option B is incorrect, as the variability of the observed sample will differ from the variability of the population due to random sampling error. Option D is incorrect, as the variability of the sampling distribution of means will be smaller than the variability of the population due to the effect of the sample size.

Which of the Following Can We Conclude If We Assume