Question

a sample is selected from a population with a mean of \\( \mu = 100 \\) and a standard deviation of \\( \sigma = 20 \\).
a. if the sample has \\( n = 16 \\) scores, what is the ex-
pected value of \\( m \\) and the standard error of \\( m \\)?

Explanation:

Step1: Find the expected value of \(M\)

The expected value of the sample mean \(M\) is equal to the population mean \(\mu\).
\(E(M)=\mu\)
Given \(\mu = 100\), so \(E(M)=100\)

Step2: Calculate the standard error of \(M\)

The formula for the standard error of the mean is \(\sigma_M=\frac{\sigma}{\sqrt{n}}\)
Given \(\sigma = 20\) and \(n = 16\)
\(\sigma_M=\frac{20}{\sqrt{16}}=\frac{20}{4}=5\)

Answer:

The expected value of \(M\) is \(100\) and the standard error of \(M\) is \(5\)