Question

The following sample of n = 4 scores was obtained from a population with unknown parameters. Scores: 2, 2, 6, 2 Compute the sample mean and standard deviation. Note: These are descriptive values that summarize the sample data. (Round your answers to two decimal places.) M = S = Compute the estimated standard error for M. (Note: This is an inferential value that describes how accurately the sample mean represents the unknown population mean.) SM =

Answer 1

$M=\frac{\sum x }{n}=\frac{2+2+6+2}{4}=\frac{12}{4}=3$

$S=\sqrt{\frac{\sum(x-\bar{x})^2 }{n-1}}=\sqrt{\frac{1+1+3^2+1}{3}}=\sqrt{\frac{12}{3}}=\sqrt{4}=2$

$S_M=\frac{S}{\sqrt{n}}=\frac{2}{\sqrt{4}}=\frac{2}{2}=1$