Lecture 9 - Summary of Forms for Null and Alternative...

Developing Null and Alternative Hypotheses
! Hypothesis testing can be used to determine whether
a statement about the value of a population parameter
should or should not be rejected.
!
The null hypothesis , denoted by H
0
, is a tentative
assumption about a population parameter.
!
The alternative hypothesis , denoted by H
a
, is the
opposite of what is stated in the null hypothesis.
! The alternative hypothesis is what the test is
attempting to establish.
One-tailed
(lower-tail)
One-tailed
(upper-tail)
Two-tailed
Summary of Forms for Null and Alternative
Hypotheses about a Population Mean
!
The equality part of the hypotheses always appears
in the null hypothesis.
! In general, a hypothesis test about the value of a
population mean μ must take one of the following
three forms (where μ
0
is the hypothesized value of
the population mean).
!
Example: Metro EMS
Null and Alternative Hypotheses
Operating in a multiple
hospital system with
approximately 20 mobile medical
units, the service goal is to respond to medical
emergencies with a mean time of 12 minutes or less.
A major west coast city provides
one of the most comprehensive
emergency medical services in
the world.
The director of medical services
wants to formulate a hypothesis
test that could use a sample of
emergency response times to
determine whether or not the
service goal of 12 minutes or less
is being achieved.
!
Example: Metro EMS
Null and Alternative Hypotheses

Null and Alternative Hypotheses
The emergency service is meeting
the response goal; no follow-up
action is necessary.
The emergency service is not
meeting the response goal;
appropriate follow-up action is
necessary.
H
0
: μ < 12
H
a
: μ > 12
where: μ = mean response time for the population
of medical emergency requests
Type I Error
! Because hypothesis tests are based on sample data,
we must allow for the possibility of errors.
!
A Type I error is rejecting H
0
when it is true.
!
The probability of making a Type I error when the
null hypothesis is true as an equality is called the
level of significance .
!
Applications of hypothesis testing that only control
the Type I error are often called significance tests .
Type II Error
!
A Type II error is accepting H
0
when it is false.
!
It is difficult to control for the probability of making
a Type II error.
!
Statisticians avoid the risk of making a Type II
error by using “do not reject H
0
” and not “accept H
0
”.
Type I and Type II Errors
Correct
Decision
Type II Error
Correct
Decision
Type I Error
Reject H
0
(Conclude μ > 12)
Accept H
0
(Conclude μ < 12)
H
0
True
( μ < 12)
H
0
False
( μ > 12)
Conclusion
Population Condition

p -Value Approach to
One-Tailed Hypothesis Testing
! A p -value is a probability that provides a measure
of the evidence against the null hypothesis
provided by the sample.
!
The smaller the p -value, the more evidence there
is against H
0
.