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,