Question

A researcher selects all of the possible samples with n = 8 scores from a population and computes the mean, dividing by n, for each sample. If the population mean is μ = 14, then what is the average value for all of the sample means?

Answer 1

Answer:

By the Central Limit Theorem, the average value for all of the sample means is 14.

Step-by-step explanation:

We use the central limit theorem to solve this question.

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means of size n can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error $s = \frac{\sigma}{\sqrt{n}}$

If the population mean is μ = 14, then what is the average value for all of the sample means?

By the Central Limit Theorem, the average value for all of the sample means is 14.