Which of the following is a true statement about the Central Limit Theorem for sample means?
A)If the sample size is large, it doesn't matter what the distribution of the population it was drawn from is, the normal distribution can still be used to perform statistical inference.
B)If conditions are met, the mean of the sampling distribution is equal to the population mean.
C)The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random sample from a population.
D)All of the statements are true about the Central Limit Theorem for sample means.

Question

Quizplus · Accepted Answer

The Central Limit Theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size becomes large, regardless of the population's distribution. This allows for the use of normal distribution in statistical inference (A). It also ensures that the mean of the sampling distribution equals the population mean (B), and it is indeed used to find probabilities for sample means based on random samples (C). Therefore, all statements (A, B, and C) are true reflections of the CLT's implications.

Which of the Following Is a True Statement About the Central