This hypothesis is called the
null hypothesis
, denoted by
0
H
.
The
null hypothesis (
0
H
) is a statement about the value of a population parameter which is assumed
to be true unless sample results imply that it is not.
Contrasting to the null hypothesis is the
alternative hypothesis
, denoted by
1
H
. For example, we
could set up the following alternative hypothesis:
The mean weight of JC2 male students is more than 70 kg.
Usually, we are hoping to reject null hypothesis and the alternative hypothesis is what we want to
establish.
In order to test the validity of
0
H
, we consider observations made from a random sample taken from
the population and perform a
statistical test
. We write the above statements concisely as
0
H
:
= 70
vs
1
H
:
> 70
8.1.2
1-Tail and 2-Tail Tests
There are two types of test that can be performed, depending on the alternative hypothesis being made.
These are
1-tail
or
2-tail
tests.
(i)
A
1-tail test
is performed when the alternative hypothesis considers an increase or a
decrease in the population parameter;
(ii)
A
2-tail test
is performed when the alternative hypothesis considers any change in the
parameter (either an increase or a decrease).
For testing of population mean, we formulate the null and alternative hypothesis as follows:
Null Hypothesis:
0
H
:
0
(note:
0
is the assumed population mean)
Alternative Hypothesis:
1
H
:
0
(any change)
2-tail test
1
H
:
0
(definite increase)
1
H
:
0
(definite decrease)
Example 8.1 :
For each of the following situations in (a) to (c), write down the null and alternative hypothesis, and.
state whether they are one or two-tailed tests.
a)
A machine packs flour into bags, with average mass, which are supposed to be 1000 g. After
adjustments to the machine, the bags have mass that are more than 1000 g.
1-tail test

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