Russel-Research-Method-in-Anthropology

182 Chapter 7
In January 2005, the Gallup Poll reported that 38% of Americans over 18
years of age report keeping one or more guns in their home (down from about
47% in 1959 and from 40% in 1993). The poll included 1,012 respondents
and had, as the media say, a ‘‘margin of error of plus or minus three percentage
points.’’ This point estimate of 38% means that 385 of the 1,012 people
polled said that they had at least one gun in their house.
We can calculate the confidence interval around this point estimate. From
the central limit theorem, we know that whatever the true proportion of people
is who keep a gun in their home, the estimates of that proportion will be normally
distributed if we take a large number of samples of 1,012 people. The
formula for determining the 95% confidence limits of a point estimator is:
P (the true proportion) 1.96PQ/n Formula 7.4
We use an italicized letter, P, to indicate the true proportion. Our estimate is
the regular uppercase P and Q is 1 P. Table 7.4 shows what happens to the
TABLE 7.4
Relation of P, Q, and PQ
If the value of P is really Then PQ is and PQ is
.10 or .90 .09 .30
.20 or .80 .16 .40
.30 or .70 .21 .46
.40 or .60 .24 .49
.50 .25 .50
square root of PQ as the true value of P goes up from 10% to 90% of the
population.
We can use our own estimate of P from the Gallup poll in the equation for
the confidence limits. Substituting .38 for P and .62 (1 .38) for Q, we get:
P P 1.96 (.38)(.62)/1,012 .38 .0299
which, with rounding, is the familiar ‘‘plus or minus three percentage points.’’
This means that we are 95% confident that the true proportion of adults in the
United States who had at least one gun in their home (or at least said they did)
at the time this poll was conducted was between 35% and 41%.
Suppose we want to estimate P to within plus or minus 2 percentage points
instead of 3 and we still want to maintain the 95% confidence level. We substitute
in the formula as follows:
P P 1.96(.38)(.62)/n .02