# Error analysis

1. Dec 19, 2006

### stunner5000pt

1. The problem statement, all variables and given/known data
A student makes 10 measurements of length x and gets the results all in mm

46,48,44,38,45,47,58,44,45,43

Using cahuvenenet's criterion should he accept or reject the measurement of 58??

2. Relevant equations
$\overline{x}$ = average
$sigma_{x}$ = standard deviation
$x_{sus}$ = the measurement we want to reject or accept
$$t_{sus} = \frac{x_{sus}-\overline{x}}{\sigma_{x}}$$
the number of standard deviationsfrom which x sus differes from x bar
n(worse than $x_{sus}$) = N P(outside $t_{sus} \sigma_{x}$)

is n < 0.5 then 58 is rejected

if n > 0.5 then 58 is accepted
3. The attempt at a solution
well the average
x bar = 45.8
$$t_{sus} = 2.4$$ standard deviations

then
P(putside 2.4$\sigma$) = 1 - P(within 2.4 $\sigma$)
= 1 - 0.984
the 0.984 is taken from a table which shows the percent probability
P(within $t\sigma$)= \int_{X-t\sigma}^{X+t\sigma} f_{X,\sigma} (x) dx [/tex], as a function of t

but why is .984?? Why is it that the probability should be chonse to be 0.01 and not 0.00 ... or 0.02??