Standard error

The standard error of the mean of a sample from a population is defined as:

${\frac {\sigma _{X}}{\sqrt {n}}}$ is (an estimation of) the standard deviation of $X$ and is called the Standard error. As example imaging that the time spend in traffic by employees has a mean of 60 and a standard deviation of 20. If employees are selected at random, what is the probability that the sample average will be over 64 minutes if the sample size is (a) 40 or (b) 100.

a) With sample of 40 we have: standard error = ${\frac {20}{{\sqrt {4}}0}}$ = 3.162278 and Z = ${\frac {X-\mu }{\sigma }}$ = ${\frac {64-60}{3.162278}}$ = 1.2649 Looking up this value in Standard Normal Distribution Table we find a value of 1 - 0.5 - 0.3962 = 0.1038 (~10%)

b) With sample of 100 we have: standard error = ${\frac {20}{{\sqrt {1}}00}}$ = 2 and Z = ${\frac {X-\mu }{\sigma }}$ = ${\frac {64-60}{2}}$ = 2 Looking up this value in Standard Normal Distribution Table we find a value of 1 - 0.5 - 0.4772 = 0.0228 (~2%)

Part of: M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals Seel also: http://en.wikipedia.org/wiki/Standard_error_%28statistics%29