Compute the confidence interval for the mean length of gizmo

Compute the confidence interval for the mean length of “gizmos”, with the additional constraint that the width of the interval must not exceed 1 mm (one millimeter).

A preliminary sample of 20 gizmos yields a mean of 73 mm. The measuring process has a variance (s2) of 6 mm2.

What is the minimum sample size required to satisfy all the constraints stated above?

Solution

Compute Sample Size
AT CONFIDENCE 95%
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 6
ME =1
n = ( 1.96*6/1) ^2
= (11.76/1 ) ^2
= 138.3 ~ 139      

AT CONFIDENCE 99%
n = ( 2.58*6/1) ^2
= (15.48/1 ) ^2
= 239.63 ~ 240      

AT CONFIDENCE 90%   
ME =1
n = ( 1.64*6/1) ^2
= (9.84/1 ) ^2
= 96.83 ~ 97