Introductory Biostatistics

samples (n>25,nshould be much larger for a narrow intervals; procedures for
small samples are rather complicated and are not covered in this book).

Example 4.8 Consider the problem of estimating the prevalence of malignant
melanoma in 45- to 54-year-old women in the United States. Suppose that a
random sample ofn¼5000 women is selected from this age group andx¼ 28
are found to have the disease. Our point estimate for the prevalence of this
disease is

p¼

28

5000

¼ 0 : 0056

Its standard error is

SEðpÞ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð 0 : 0056 Þð 1 
 0 : 0056 Þ

5000

r

¼ 0 : 0011

Therefore, a 95% confidence interval for the prevalencepof malignant mela-
noma in 45- to 54-year-old women in the United States is given by

0 : 0056 Gð 1 : 96 Þð 0 : 0011 Þ¼ð 0 : 0034 ; 0 : 0078 Þ

Example 4.9 A public health o‰cial wishes to know how e¤ective health
education e¤orts are regarding smoking. Ofn 1 ¼100 males sampled in 1965 at
the time of the release of the Surgeon General’s Report on the health con-
sequences of smoking,x 1 ¼51 were found to be smokers. In 1980 a second
random sample ofn 2 ¼100 males, gathered similarly, indicated thatx 2 ¼ 43
were smokers. Application of the method above yields the following 95% con-
fidence intervals for the smoking rates:

(a) In 1965, the estimated rate was

p 1 ¼

51

100

¼ 0 : 51

with its standard error

SEðp 1 Þ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð 0 : 51 Þð 1 
 0 : 51 Þ

100

r

¼ 0 : 05

162 ESTIMATION OF PARAMETERS