
110 Data Analysis and Statistics for Geography, Environmental Science, and Engineering
4.5 PARAMETRIC METHODS
4.5.1 Z test or stanDarD norMal
We use this parametric method to test whether the sample mean is different from the population
mean (parameter). It assumes a known distribution (normal) with known parameters mean μ
X
and
variance = σ
X
2
. We build the statistic z by the ratio of deviations of the sample mean from hypotheti-
cal or population mean to the standard error σ
e
.
Z
n
X
e
X
X
=
=
σ
σ /
(4.12)
The null hypothesis is H0: X
–
= μ
X
. If z is large for given α, then reject H0; if the z value indicates
that H0 cannot be rejected, then there is ...