Question

A random sample of n = 4 scores is selected from a population with mean (mu) = 80 and population standard deviation (sigma) = 20. On average, how much difference would you expect between the sample mean and the population mean? (i.e., What is the standard error of a sampling distribution composed of means taken from samples of size 4?)

Answer 1

Answer: 10

Step-by-step explanation:

The formula used for standard error is :-

$\sigma_x=\dfrac{\sigma}{\sqrt{n}}$, where $\sigma$ is population standard deviation and n is the sample size.

Given: n = 4

$\sigma=20$

Then, the  difference would expected between the sample mean and the population mean will be :

$\sigma_x=\dfrac{20}{\sqrt{4}}=\dfrac{20}{2}=10$

Hence, the expected difference between the sample mean and the population mean = 10

Answer 2

The standard error of the given sample distribution is; 10

What is Standard Error?

We are given;

Sample size; n = 4

Sample mean; μ = 80

Standard deviation; σ = 20

Formula for the standard error is;

σₓ = σ/√n

σₓ = 20/√4

σₓ = 10

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