Z-Test
Z-test is a statistical test where
normal distribution is applied and is basically used for dealing with problems
relating to large samples when n ≥ 30.
n = sample size
For example suppose a person wants
to test if both tea & coffee are equally popular in a particular town. Then
he can take a sample of size say 500 from the town out of which suppose 280 are
tea drinkers. To test the hypothesis, he can use Z-test.
Z-TEST’S
FOR DIFFERENT PURPOSES
There are different types of Z-test each for different purpose.
Some of the popular types are outlined below:
- z test for single proportion is used to test a hypothesis on a specific value
of the population proportion.
Statistically
speaking, we test the null hypothesis H0:
p = p0 against the alternative hypothesis H1: p >< p0 where p
is the population proportion and p0 is a specific value of the
population proportion we would like to test for acceptance.
The
example on tea drinkers explained above requires this test. In that example, p0 =
0.5. Notice that in this particular example, proportion refers to the
proportion of tea drinkers.
- z test for difference of proportions is used to test the hypothesis that two
populations have the same proportion.
For
example suppose one is interested to test if there is any significant
difference in the habit of tea drinking between male and female citizens of a
town. In such a situation, Z-test for difference of proportions can be applied.
One would
have to obtain two independent samples from the town- one from males and the
other from females and determine the proportion of tea drinkers in each sample
in order to perform this test.
- z -test for single mean is used to test a hypothesis on a specific value
of the population mean.
Statistically
speaking, we test the null hypothesis H0: μ = μ0 against
the alternative hypothesis H1: μ >< μ0 where μ
is the population mean and μ0 is a specific value of the
population that we would like to test for acceptance.
Unlike the
t-test for single mean, this test is used if n ≥ 30 and population standard deviation is known.
- z test for single variance is used to test a hypothesis on a specific value
of the population variance.
Statistically
speaking, we test the null hypothesis H0: σ = σ0 against
H1: σ >< σ0 where σ is the population mean and
σ0 is a specific value of the population variance that we would
like to test for acceptance.
In other
words, this test enables us to test if the given sample has been drawn from a
population with specific variance σ0. Unlike the chi square test for
single variance, this test is used if n ≥ 30.
- Z-test for testing equality of variance is used to test the hypothesis of equality of
two population variances when the sample size of each sample is 30 or
larger.
By: Lera Gay Bacay
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