Question

Which of the following is true about The Central Limit Theorem?

a. the shape of the sampling distribution gets wider with a larger sample size
b. the shape of the sampling distribution gets shorter with a larger sample size
c. the shape of the sampling distribution will not change the larger the sample size is
d. the shape of the sampling distribution will approximate a normal curve the larger the sample size is

Answer 1

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution.

Step-by-step explanation:

The question is regarding the Central Limit Theorem, an important concept in statistics. Among the options given about what is true about the Central Limit Theorem, the correct choice is that the shape of the sampling distribution will approximate a normal curve the larger the sample size is (option d). This is because as the sample size increases, the sampling distribution of the sample means will approach normality, which is a fundamental aspect of the Central Limit Theorem. This theorem holds true regardless of whether the population distribution itself is normal. Furthermore, with larger samples, the standard deviation of the sampling distribution, or the standard error, gets smaller because it is equal to the population standard deviation divided by the square root of the sample size.