| The z-test is a hypothesis
test used to test the mean
against a specified value. The z-test 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:
H0 the population mean equals
a specified value
H1 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 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 of the
z statistic can be found from tables. For
a one sided test:
| α
|
0.10 |
0.05 |
0.025 |
0.01 |
| Zα
|
1.28 |
1.64 |
1.96 |
2.33 |
For samples less than 30 use
the t-test.
|
