Introductory Biostatistics

Therefore,

pvalue¼Prðpa 0 :15 orpb 0 : 35 Þ

¼ 2 Prðpb 0 : 35 Þ

¼ 2 Pr zb

0 : 35
0 : 25

0 : 043



¼ 2 Prðzb 2 : 33 Þ

¼ð 2 Þð 0 : 5 
 0 : 4901 Þ

F 0 : 02

In other words, with the data given, the di¤erence between the national smok-
ing rate and the smoking rate of New England states is statistically significant
(p< 0 :05).

5.3.3 Relationship to Confidence Intervals

Suppose that we consider a hypothesis of the form

H 0 :m¼m 0

wherem 0 is a known hypothesized value. A two-sided hypothesis test forH 0 is
related to confidence intervals as follows:

1. Ifm 0 is not included in the 95% confidence interval form,H 0 should be
   rejected at the 0.05 level. This is represented graphically as shown in
   Figure 5.7.


2. Ifm 0 is included in the 95% confidence interval form,H 0 should not be
   rejected at the 0.05 level (Figure 5.8).

Example 5.3 Consider the hypothetical data set in Example 5.2. Our point
estimate of smoking prevalence in New England is

Figure 5.6 Graphical display of thepvalue for Example 5.2.

SUMMARIES AND CONCLUSIONS 201