| Hypothesis
Test for Proportions |
|
The hypothesis test for proportions
is a type of hypothesis test used
to compare proportions.
The tests in this topic are
used when the sample sizes are reasonably
large, and so the binomial distribution
can be approximated by the normal distribution.
If the sample sizes are small an alternative
is to use a Chi-Square test.
This test is used for large samples to
test the hypothesis:
H0: the proportion is the
same in both populations
H1: the proportions are different/the
proportion is greater for process 1 than
process 2
The value of the Z statistic
is calculated from:
where:
p1 and p2: the
proportions in each sample
X1 and X2: the number
possessing the characteristic in each
sample
n1 and n2: the sample
size
The p-value can be obtained
from Excel using the function:
one-tail test: = 1 - NORMSDIST(Z0)
two-tail test: = (1 -
NORMSDIST(Z0))/2
Alternatively the critical
values can be found in the t-tables.
| Proportion
Against a Specified Value |
|
This test is used for large samples to
test the hypothesis:
H0: the proportion is the
same in both populations
H1: the proportion is [different
to/greater than/less than] the specified
value
The value of the Z statistic
is calculated from:
the proportion in the sample
the specified value of the proportion
n the sample size
The p-value can be obtained from Excel
using the function:
one-tail test: = 1 - NORMSDIST(Z0)
two-tail test: = (1 -
NORMSDIST(Z0))/2
Alternatively the critical values can
be found in the t-tables.
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