A process for making certain bearings is under control if th

A process for making certain bearings is under control if the diameters of the bearings have a mean of 0.5000 cm. What can we say about this process if a sample of 10 of these bearings has a mean diameter of 0.5060 cm and a standard deviation of 0.0040 cm?

Solution

FOR 95% CONFIDENCE:

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
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 =    0.506          
t(alpha/2) = critical t for the confidence interval =    2.262157163          
s = sample standard deviation =    0.004          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
Margin of Error E =    0.002861428          
Lower bound =    0.503138572          
Upper bound =    0.508861428          
              
Thus, the confidence interval is              
              
(   0.503138572   ,   0.508861428   )

As 0.5000 is not inside this interval, then the process is probably out of control. [CONCLUSION]