# The following sample was obtained from a population with unknown param

The following sample was obtained from a population with unknown parameters. Scores: 13, 7, 6, 12, 0, 4 a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.) b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)
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Clis1955
Step 1
a) The sample mean and sample standard deviation can be calculated as:
$Mean\left(\stackrel{―}{x}\right)=\frac{\text{Sum of observations}}{\text{Number of observations}}$
$=\frac{13+7+6+12+0+4}{6}$
$=\frac{42}{6}$
$\stackrel{―}{x}=7$
So, $s=\sqrt{\frac{\sum _{i=1}^{n}{\left({x}_{i}-\stackrel{―}{x}\right)}^{2}}{n-1}}$
$=\sqrt{\frac{{\left(13-7\right)}^{2}+{\left(7-7\right)}^{2}+{\left(6-7\right)}^{2}+{\left(12-7\right)}^{2}+{\left(0-7\right)}^{2}{\left(4-7\right)}^{2}}{6-1}}$
$=10.03$
Therefore, the sample mean and standard deviation are 7 and 10.03 respectively.
Step 2
b) The estimated error for the mean is.
$SE=\frac{s}{\sqrt{n}}$
$=\frac{10.03}{\sqrt{6}}$
$=4.09$
Therefore, the estimated standard error for M is 4.09.