Introduction to Probability and Statistics for Engineers and Scientists

476 Chapter 10:Analysis of Variance

next 3 weeks. The second group was instructed to eat a particular type of high-fiber

whole-grain cereal for the next 3 weeks. The final group was instructed to eat as

they normally do. After the 3-week period elapsed, the nutritionist had each of the

bicyclists ride 6 miles. The following times were recorded.

Vitamin group: 15.6 16.4 17.2 15.5 16.3

Fiber cereal group: 17.1 16.3 15.8 16.4 16.0

Control group: 15.9 17.2 16.4 15.4 16.8

(a) Are the data consistent with the hypothesis that neither the vitamin nor

the fiber cereal affected the bicyclists’ speeds? Use the 5 percent level of

significance.

(b) Find confidence intervals for all quantitiesμi−μjthat, with 95 percent

confidence, are valid.

15.Test the hypothesis that the following three independent samples all come from

the same normal probability distribution.

Sample 1 Sample 2 Sample 3

35 29 44

37 38 52

29 34 56

27 30

30 32

16.For dataxij,i=1,...,m,j=1,...,n, show that

x..=

∑m

i= 1

xi./m=

∑n

j= 1

x.j/n

17.Ifxij=i+j^2 , determine

(a)

∑ 3

j= 1

∑ 2

i= 1 xij

(b)

∑ 2

i= 1

∑ 3

j= 1 xij

18.Ifxij=ai+bj, show that

∑m

i= 1

∑n

j= 1

xij=n

∑m

i= 1

ai+m

∑n

j= 1

bj

19.A study has been made on pyrethrum flowers to determine the content of pyrethrin,

a chemical used in insecticides. Four methods of extracting the chemical are used,