Question

The following sample was obtained from a populationwith unknown parameters. Scores: 13, 7, 6, 12, 0, 4a. Compute the sample mean and standard deviation.(Note that these are descriptive values that sum-marize the sample data.)b. Compute the estimated standard error for M. (Notethat this is an inferential value that describes howaccurately the sample mean represents the un-known population mean.)

Answer 1

a.

The mean of a sample is given by:

`\bar{x}=(\sum_(i=1)^nx_i)/(n)`

In this case we have:

`\begin{gathered} \bar{x}=(13+7+6+12+0+4)/(6) \\ \bar{x}=(42)/(6) \\ \bar{x}=7 \end{gathered}`

Therefore, the mean of the sample is 7

The standard deviation is:

`s=\sqrt{\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}{n-1}}`

Then we have:

`\begin{gathered} s=\sqrt{((13-7)^2+(7-7)^2+(6-7)^2+(12-7)^2+(0-7)^2+(4-7)^2)/(6-1)} \\ =\sqrt{(36+0+1+25+49+9)/(5)} \\ =\sqrt{(120)/(5)} \\ =√(24) \end{gathered}`

Therefore, the standard deviation is √24

b.

The standard error is defined as:

`SE=(s)/(√(n))`

Then we have:

`SE=(√(24))/(√(6))=\sqrt{(24)/(6)}=√(4)=2`

Therefore, the estimated standard error is 2