The test for comparing proportions
is used to test whether differences in the
proportions of a characteristic that occur
in two samples are sufficient to prove that
the populations from which the samples were
taken are different. It is used when the
samples are large.
The hypothesis
is:
H_{0}: the proportion is the
same in both populations
H_{1}: the proportions are different/the
proportion is greater for process 1 than
process 2
The value of the Z statistic
is calculated from:
where:
p_{1} and p_{2}: the
proportions in each sample
X_{1} and X_{2}: the number
possessing the characteristic in each
sample
n_{1} and n_{2}: the sample
size
The pvalue
can be obtained from Excel using the function:
twotail test: = (1 
NORMSDIST(Z_{0}))/2
Alternatively the critical
values can be found in the ttables.
