In addition, we have
A¼ 350
B¼ 390
n 1 ¼ 130
n 2 ¼ 335
n 3 ¼ 235
n 4 ¼ 40
N¼ 740
Substituting these values into the equations of the test statistic, we have
S¼ 53 ; 225 40 ; 025
¼ 13 ; 200
sS¼
ð 350 Þð 390 Þ
ð 3 Þð 740 Þð 739 Þ
ð 7403 1303 3353 2353 403 Þ
1 = 2
¼ 5414 : 76
leading to
z¼
13 ; 200
5414 : 76
¼ 2 : 44
which shows a high degree of significance (one-sidedpvalue¼ 0 :0073). It is
interesting to not that in order to compare the extent of injury from those who
used seat belts and those who did not, we can perform a chi-square test as pre-
sented in Section 6.6. Such an application of the chi-square test yields
X^2 ¼ 9 : 26
with 3 df is 7.81 (for 0: 01 apa 0 :05). Therefore, the di¤erence between the
two groups is significant at the 5% level but not at the 1% level, a lower degree
of significance (compared to thepvalue of 0.0073 above). This is because the
usual chi-square calculation takes no account of the fact that the extent of
injury has a natural ordering: none<minor<major<death. In addition, the
percent of seat belt users in each injury group decreases from level ‘‘none’’ to
level ‘‘death’’:
232 COMPARISON OF POPULATION PROPORTIONS