Question

A population has a mean μ and standard deviation σ. A sampling distribution of sample means can be created by taking samples of n items at a time. Which of the following statements will be true about the sampling distribution of sample means?

(A) It will have a population mean that is equal to μ.
(B) It will have a population mean that is less than μ.
(C) It will have a population mean that is greater than μ.
(D) It will have a population standard deviation that is equal to σ.
(E) It will have a population standard deviation that is greater than σ.
(F) It will have a population standard deviation that is less than σ.

Answer 1

The sampling distribution of sample means will have a population mean that is equal to μ.

Step-by-step explanation:

The statement that will be true about the sampling distribution of sample means is (A) It will have a population mean that is equal to μ. The sampling distribution of sample means follows the Central Limit Theorem, which states that if the sample size is sufficiently large, the distribution of the sample means will be approximately normal, and the mean of the sample means will equal the population mean μ.

In other words, as the sample size increases, the sample means tend to cluster around the population mean. This allows researchers to make inferences about the population based on the sample data. So, option (A) is correct.