Introductory Biostatistics

Let’s focus on the sample of men with a high school education; investigations
of other groups and the di¤erences between them are given in the exercises at
the end of this chapter. An application of the one-samplettest yields

x¼ 1 : 38

sx¼ 1 : 53

SEðxÞ¼

1 : 53

ffiffiffiffiffiffiffiffi

476

p

¼ 0 : 07

t¼

1 : 38

0 : 07

¼ 19 : 71

It can be easily seen that the di¤erence between self-reported height and mea-
sured height is highly statistically significant (p< 0 :01: comparing 19.71 versus
the cutpoint of 2.58 for a large sample).

7.3 COMPARISON OF TWO MEANS

Perhaps one of the most common problems in statistical inference is a com-
parison of two population means using data from two independent samples; the
sample sizes may or may not be equal. In this type of problem, we have two
sets of continuous measurents, one of sizen 1 and one of sizen 2 , and we con-
sider the null hypothesis

H 0 :m 1 ¼m 2

expressing the equality of the two population means.
To perform a test of significance forH 0 , we proceed with the following steps:

1. Decide whether a one-sided test, say

HA:m 2 >m 1

or a two-sided test,

HA:m 10 m 2

is appropriate.

2. Choose a significance levela, a common choice being 0.05.


3. Calculate thetstatistic,

COMPARISON OF TWO MEANS 253