Introductory Biostatistics

t¼

ð
 0 : 20 Þ
ð
 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:

1. For unexposed infants:

n 1 ¼ 7

x 1 ¼ 31 : 29

s 1 ¼ 37 : 07

2. 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