t¼
ð 0 : 20 Þð 0 : 26 Þ
0 : 022
¼ 2 : 73
The result indicates that the di¤erence is statistically significant beyond the 0.01
level (ata¼ 0 :01, and for a two-sided test the cut point is 2.58 for high df
values).
Example 7.7 The extend to which an infant’s health is a¤ected by parental
smoking is an important public health concern. The following data are the uri-
nary concentrations of cotinine (a metabolite of nicotine); measurements were
taken both from a sample of infants who had been exposed to household
smoke and from a sample of unexposed infants.
Unexposed (n 1 ¼7) 8 11 12 14 20 43 111
Exposed (n 2 ¼8) 35 56 83 92 128 150 176 208
The statistics needed for our two-samplettest are:
- For unexposed infants:
n 1 ¼ 7
x 1 ¼ 31 : 29
s 1 ¼ 37 : 07
- For exposed infants:
n 2 ¼ 8
x 2 ¼ 116 : 00
s 2 ¼ 59 : 99
To proceed with a two-samplettest, we have
s^2 p¼
ð 6 Þð 37 : 07 Þ^2 þð 7 Þð 59 : 99 Þ^2
13
¼ð 50 : 72 Þ^2
SEðx 1 x 2 Þ¼ð 50 : 72 Þ
ffiffiffiffiffiffiffiffiffiffiffi
1
7
þ
1
8
r
¼ 26 : 25
t¼
116 : 00 31 : 29
26 : 25
¼ 3 : 23
256 COMPARISON OF POPULATION MEANS