15 The precision of a method is being established and the fo

15. The precision of a method is being established, and the following data are obtained 22.18, 22.25, 22.09 and 22.17%. Is 22.09% a valid measurement at the 95% confidence level?

Solution

Getting the mean and standard deviation of the data,

mean = 22.184
standard deviation = 0.062289646

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    22.184          
t(alpha/2) = critical t for the confidence interval =    2.776445105          
s = sample standard deviation =    0.062289646          
n = sample size =    5          
df = n - 1 =    4          
Thus,              
              
Lower bound =    22.10665719          
Upper bound =    22.26134281          
              
Thus, the confidence interval is              
              
(   22.10665719   ,   22.26134281   )

As 22.09 is not in this interval, then NO: IT IS NOT AN ACCEPTABLE MEASUREMENT AT 95% CONFIDENCE LEVEL.