Introduction to Probability and Statistics for Engineers and Scientists

Problems 471

Problems

1. A purification process for a chemical involves passing it, in solution, through a
   resin on which impurities are adsorbed. A chemical engineer wishing to test the
   efficiency of 3 different resins took a chemical solution and broke it into 15 batches.
   She tested each resin 5 times and then measured the concentration of impurities
   after passing through the resins. Her data were as follows:

Concentration of Impurities

Resin I Resin II Resin III

.046 .038 .031

.025 .035 .042

.014 .031 .020

.017 .022 .018

.043 .012 .039

Test the hypothesis that there is no difference in the efficiency of the resins.

2. We want to know what type of filter should be used over the screen of a cathode-
   ray oscilloscope in order to have a radar operator easily pick out targets on the
   presentation. A test to accomplish this has been set up. A noise is first applied to
   the scope to make it difficult to pick out a target. A second signal, representing the
   target, is put into the scope, and its intensity is increased from zero until detected
   by the observer. The intensity setting at which the observer first notices the target
   signal is then recorded. This experiment is repeated 20 times with each filter. The
   numerical value of each reading listed in the table of data is proportional to the
   target intensity at the time the operator first detects the target.

Filter No. 1 Filter No. 2 Filter No. 3

90 88 95

87 90 95

93 97 89

96 87 98

94 90 96

88 96 81

90 90 92

84 90 79

101 100 105

96 93 98

90 95 92

(continued )