Russel-Research-Method-in-Anthropology

Univariate Analysis 589
lation, 68.26% of the statistics for estimating parameters will fall within one
standard error of the actual parameter; 95% of the estimates will fall between
the mean and 1.96 standard errors; and 99% of the estimates will fall between
the mean and 2.58 standard errors.
In table 19.2, I showed you a small sample of the data from the study that
Ryan, Borgatti, and I did (Bernard et al. 1999) on attitudes about environmental
activism. In that study, we interviewed a random sample of 609 adults from
across the United States. The mean age of respondents in our sample was
44.21, sd 15.75. Only 591 respondents agreed to tell us their age, so the standard
error of the mean is:
15.75 / 591 0.648
Since we have a large sample, we can calculate the 95% confidence limits
using the z distribution in appendix B:
44.211.96(0.648) 44.211.27 42.94 and 44.211.27 45.48
In other words, we expect that 95% of all samples of 591 taken from the
population of adults in the United States will fall between 42.94 and 45.48.
As we saw in chapter 7, these numbers are the 95% confidence limits of the
mean. As it happens, we know from the U.S. Census Bureau that the real average
age of the adult (over-18) population in the United States in 1997 (when
the survey was done) was 44.98.
Thus: (1) the sample statistic (x 44.21%) and (2) the parameter (
44.98%) both fall within the 95% confidence limits, and we can not reject the
null hypothesis that our sample comes from a population whose average age
is equal to 44.98%.
More about z-Scores
As we saw also in chapter 7 on sampling, every real score in a distribution
has a z-score, also called a standard score. Az-score tells you how far, in
standard deviations, a real score is from the mean of the distribution. The formula
for finding a z-score is:
z
(raw score x)
SD
Formula 19.9
To find the z-scores of the data on FEMILLIT in table 19.7, subtract 19.49
(the mean) from each raw score and divide the result by 20.81 (the sd). Table
19.12 shows these z-scores.