Question
Surfactants (detergents) are chemical agents that lower the surface tension of a liquid. Surfactants play an important role in the cleaning of contaminated soils. An experiments is designed to determine the effectiveness of a new method for removing toluene from sand. The sand is washed with a surfactant, and then rinsed with de-ionized water. Of interest is the amount of toluene that comes out in the rinse. Assuming that a dependable value for the standard deviation of the amount of toluene removed in the rinse cycle expressed as a percentage of the total amount originally present is 4.0%, how large a sample size is required to ensure that the resulting 90% CI for the true average percentage of toluene removed in the rinse has a width of 2.0%?
Explanation / Answer
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.664 ( From Standard Normal Table )
Standard Deviation ( S.D) = 0.04
ME =0.02
n = ( 1.664*0.04/0.02) ^2
= (0.067/0.02 ) ^2
= 11.076 ~ 12
