The Null and Alternative Hypotheses

The Null and
Alternative
Hypotheses
1 Hypothesis Testing
a statistical method of using
sample data to determine the
probability that a given
hypothesis about the population
is true.
Steps in Hypothesis Testing:
1 a.Formulate the null and alternative
hypotheses.
b.Determine the level of significance.
c.Calculate the test statistic and identify the
rejection region.
d.Make a decision.
e.Draw a conclusion.
2 Statistical Hypothesis
a statement about a population
parameter
Example:
The daily mean number of clients in an payment

center is 74.
Null Hypothesis

3
the hypothesis that is assumed
to be true. It uses a relation
symbol with a statement of
equality, such as and , and is
denoted by .
Example:

The average life expectancy of

females is the same as the
average life expectancy of males.
()
Alternative Hypothesis

4
the hypothesis that is contrary to
the null hypothesis. It uses a
relation symbol with no statement
of equality, such as and , and is
denoted by .
Example:

The average life expectancy of

females is different from the
average life expectancy of males. ()
5 Directional Test of Hypothesis
or One-tailed Test
a type of hypothesis test that makes
use of only one side or tail of the
distribution. It can either be a right-
tailed or left-tailed test.
6 Right-tailed Test
a type of directional test of hypothesis or one-
tailed test that is used when an assertion is made
that the parameter falls within the positive end of
the distribution. In a right-tailed test, the
alternative hypothesis uses comparatives such as
greater than, higher than, better than, superior to,
exceeds, above, increased, etc.

Example:
The mean number of hours students spend

studying after school is at most 2.5 hours. ()

studying after school is greater than 2.5 hours. ()
Left-tailed Test
a type of directional test of hypothesis or one-
tailed test that is used when an assertion is
made that the parameter falls within the
negative end of the distribution. In a left-tailed
test, the alternative hypothesis uses
comparatives such as less than, smaller than,
inferior to, lower than, below, decreased, etc.

Example:
The mean number of hours students spend studying

after school is at least 2.5 hours.
()
The mean number of hours students spend studying

after school is less than 2.5 hours.
()
Non-directional Test of Hypothesis
or Two-tailed Test
a type of hypothesis test that makes use of two
opposite sides or tails of the distribution. It is used
when no assertion is made on whether the
parameter falls within the positive or negative end
of the distribution. In a two-tailed test, the
alternative hypothesis uses comparatives such as
not equal to, different from, not the same as, etc.
Example:


studying after school is equal to 2.5 hours. ()

studying after school is not 2.5 hours. ()
Level of Significance

the probability of rejecting the

null hypothesis in favor of the
alternative hypothesis when it
is really true, denoted by
In hypothesis testing, the researcher
decides what level of significance to use at
the beginning of the test. Conventional
significance levels such as 0.05 and 0.01
are frequently used in hypothesis testing
because of the desire to maintain a low
probability of rejecting the null hypothesis
when it is actually true.
Example:

A significance level of means that

there is a 5% chance of rejecting a
true null hypothesis. In other words,
we are 95% confident that a right
decision is made.
Rejection Region
the set of values in which
the null hypothesis is
rejected
Example 1: A researcher wants
to test whether there is a
significant difference between
the mean frequency of exercise
between young and old people.
State the null and alternative
hypotheses.
Solution:

Let and be the population mean frequency of exercise of

young and old people, respectively. The hypotheses can be
stated as:

There is no significant difference between the mean frequency
of exercise of young and old people. ()

There is a significant difference between the mean frequency
of exercise of young and old people. ()
Example 2: A store owner wants
to know if the daily average
number of customers in the
clothing shop is greater than
246. State the null and
alternative hypotheses.
Solution:

Let be the population daily mean number of

customers in the clothing shop. The hypotheses can
be stated as:

The daily mean number of customers in the clothing
shop is less than or equal to 246. ()

The daily mean number of customers in the clothing
shop is greater than 246. ()
Individual Practice:
1. Researcher A claims that an average professional typist

has a mean typing speed of 75 words per minute.
Researcher B wants to test whether this claim is true.
State the null and alternative hypotheses.
2. A teacher wants to test the claim that female students

have less absences compared to male students. State
the null and alternative hypotheses.

The Null and Alternative Hypotheses

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The Null and

The daily mean number of clients in an payment

The average life expectancy of

The average life expectancy of

The mean number of hours students spend

The mean number of hours students spend

The mean number of hours students spend studying

The mean number of hours students spend studying

The mean number of hours students spend

The mean number of hours students spend

the probability of rejecting the

A significance level of means that

Let and be the population mean frequency of exercise of

Let be the population daily mean number of

1. Researcher A claims that an average professional typist

2. A teacher wants to test the claim that female students

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