Help on probability

[saidm]

Hi every body,
Can some one help with the calcul of Risk (probability expressed by %) of having measurements falling outside of the acceptance limits fixed to 5%.
here after the measurements (N=12) of one variable :

1,24037
1,25665
1,24786
1,26226
1,24762
1,25524
1,25135
1,24931
1,25570
1,25156


Many thanks

 

[ShaktiRathore]

It seems a little more on calculation side can you please explain the Q more. otherwise its very calculative.

thanks

 

[saidm]

It seems a little more on calculation side can you please explain the Q more. otherwise its very calculative.

thanks

Dear ShaktiRathore,
here is the problem:
It's about a method validation. I do a series of calibration Standards (6 levels, 3 replicates per level, 3 series) and a series of validation standards (6 levels, 4 replicates per level , 3 series). For each level the back calculated concentration was calculated. Above in the first message values calculated for level 1 (1,25 mg/l), for each level i have to find the probality of having future measurements falling outside of the acceptance limits (here we fix the limits to 5%). I do not know witch formula to use for this...
Thanks for help

 

[NewComer]

Still unclear. What are the acceptance limits?

 

[saidm]

The acceptance limits are the mean value ± 5%.

 

[NewComer]

Are you FRM candidate?
If yes, you should know it…
If no, in brief:
1. Calculate mean and variance of the sample.
2. Then,
if population distribution is normal with known variance, use z-statistics for small and large samples;
if population distribution is normal with unknown variance, use t-statistics for small and large samples;
if population distribution is nonnormal with known variance, use z-statistics for large samples (n>30); no answer for small samples;
if population distribution is nonnormal with unknown variance, use t-statistics for large samples (n>30); no answer for small samples;
3. This is two-side test; z or t = 0.05*mean/sigma
4. In your case sample is small (<30), variance is unknown, so without assumption of population normality there is no answer…, with, go ahead with t-statistics.
5. Or, increase the sample and go ahead with t-statistics

Actually, this is elementary course on statistics, usually for 2nd-year students...