Question

Statistics questions.

Given a data set with n trials (n=12), how do I calculate the 99.7% confidence level?

How do I calculate the uncertainty to a 99.7% confidence level?

How do I calculate average error? Comment how the  99.7% confidence levels compares to the average error..

Answer 1

1.

here z for 99.7% is 3 and n=12

confidence interval : [ mean - 3*SD/ 3.46 , mean + 3*SD/ 3.46 ]

{SD = standard deviation}

uncertainty = (100-99.7)/100 = 0.3/100 = 0.003

uncertainty = 0.003

average error :

here x = mean , xi = i th observation , n=12

check if z*(SD)/(n^0.5) = 3*(SD)/3.46

if [ 3*(SD)/3.46 ] is less than AE then we can say average error is covered in the confidence interval otherwise not

P.S. (please upvote if you find the answer satisfactory)