Introduction to Probability and Statistics for Engineers and Scientists

Problems 473

6. Twenty overweight individuals, each more than 40 pounds overweight, were ran-
   domly assigned to one of two diets. After 10 weeks, the total weight losses (in
   pounds) of the individuals on each of the diets were as follows:

Weight Loss

Diet 1 Diet 2

22.2 24.2

23.4 16.8

24.2 14.6

16.1 13.7

9.4 19.5

12.5 17.6

18.6 11.2

32.2 9.5

8.8 30.1

7.6 21.5

Test, at the 5 percent level of significance, the hypothesis that the two diets have

equal effect.

7. In a test of the ability of a certain polymer to remove toxic wastes from water, exper-
   iments were conducted at three different temperatures. The data below give the
   percentages of the impurities that were removed by the polymer in 21 independent
   attempts.

Low Temperature Medium Temperature High Temperature

42 36 33

41 35 44

37 32 40

29 38 36

35 39 44

40 42 37

32 34 45

Testthehypothesisthatthepolymerperformsequallywellatallthreetemperatures.

Use the(a)5 percent level of significance and(b)1 percent level of significance.

8. In the one-factor analysis of variance model withnobservations per sample, letSi^2 ,
   i=1,...,mdenote the sample variances for themsamples. Show that

SSW=(n−1)

∑m

i= 1

Si^2