The ztest is a hypothesis
test used to test the mean
against a specified value. The ztest is
used where the standard deviation is known
or the sample is large (greater than about
30). The population must also conform to
a normal distribution. The hypothesis is:
H_{0} the population mean equals
a specified value
H_{1} the popular mean is [equal
to/less than/greater than] a specified
value
The test is:
where:

sample mean 
μ _{0} 
specified value 
s 
sample standard deviation 
n 
sample size 
The pvalue
can be obtained from Excel using the function:
onetail test: = 1  NORMSDIST(Z_{0})
twotail test: = (1  NORMSDIST(Z_{0}))/2
Alternatively the critical values of the
z statistic can be found from tables. For
a one sided test:
α

0.10 
0.05 
0.025 
0.01 
Z_{α
} 
1.28 
1.64 
1.96 
2.33 
For samples less than 30 use
the ttest.
