11.10 a. Do we reject the null hypothesis in analysis of
large ora small R2?
b. In addition to the actual value of W,
whether the null hypothesis is rejected or not?
c. In analysis of variance, to which statistical
convert R2 in order to find the p-value for the data?
U.18 ana ysis of variance of data on
of the 48 con tiguous states for 1994 with e ther cap1ta mcome in eacb
regions, gives the results in Table 11.g_ e states grouped into 8
a. What is the independent variable and ~hat is the dependent
variable in this analysis?
b. What conclusions can you draw from the results?
c. What are sorne things you might want to know about regions
and incomes that these results do not convey?
Table 11.9 Data for Exercise 11.18
Sumo/ Degrees of Mean
&,ura squares freedom square F.JJ"atio
Region 195.0 7 27.86 5.33
Residual 209.1 40 5.23
Tot.al 404.1 4 7
tl,24 The numbers of female and male piglets in litters concerns
Table 11.12 Data
for Exercise 11.24
ople who raise pigs. The data in Table 11.12 show the number of
remalea nd male pigs in 6 different litters. The difference between ~e
rnean number of females and the mean number of males results m
t:::: - 0.29, 10 d.f., and p = 0.39.
Litter Femal.es Males
a. What is the null hypothesis being studied here?
b. Can you conclude that there is a difference in the m~an
numbers of female and male piglets in the larger populauon
from which these data carne?
c. What aspect of the data is not taken into account in this
L--...&-.-.-.------------------- ~ -:ro. ....
l 4 5
2 6 4
3 5 5
4 3 6
5 4 4
6 6 5
SourceS: . M. Freef,r .,
U.28 In the study of Europeans cited in Exercise 11.27, people were
also asked about the satisfaction they felt with the lives they were leading.
Ranking very satisfied as 1, fairly satisfied as 2, not very satisfied as
3, and not at ali satisfied as 4, we find a mean satisfaction of 1.41 in
Denmark, 2.16 in France, 1.65 in The Netherlands, and 1.88 in West
Germany. The overall mean equals l. 77. An analysis of variance to study
these country differences gives W = 0.16 and F = 250 on 3 and 3,995
degrees of freedom. What do the results tell you about the differences
between the four countries?
¡t.42 This is a famous data
sboW in inches the heights ;ettollected by_Charles Darwin. The data
0feach pairwas cross-fertiliz:dp ants grown m 15 pairs. One member
waisn terested in whether th ªnd the other wass elf-fertilized. Darwin
ere was any dia- . h . ¡be two groups . uerence m e1ghts between
Pair 1 2 3 4 5 6 7 8
eross-fertilized 23.5 12.0 21.0 22.0 19.I
21.5 22.1 20.4
20.4 20.0 20.0 18.4 18.6 18.6 15.3
Pair 9 10 11 12 13 14 15
Cross-fertilized 18.3 21.6 23.3 21.0 22.1 23.0 12.0
Self.fertilized 16.5 18.0 16.3 18.0 12.8 15.5 18.0
~ : CharlesD arwin, The Effect of Cross- and Self-fertilization in the Vegetable
Kingdom, 2d ed., London:john Murray, 1876, p. 451.
a. Find the difference in height for each pair and test the null
hypothesis that the mean difference equals zero.
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