Download download

Matakuliah
Tahun
Versi
: I0262 – Statistik Probabilitas
: 2007
: Revisi
Pertemuan 08
Pengujian Hipotesis 1
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat memilih statistik uji
hipotesis untuk suatu dan dua rataan.
2
Outline Materi
• Uji hipotesis nilai tengah
• Uji hipotesis beda nilai tengah
3
Hypothesis Testing
• Developing Null and Alternative Hypotheses
• Type I and Type II Errors
• One-Tailed Tests About a Population Mean:
Large-Sample Case
• Two-Tailed Tests About a Population Mean:
Large-Sample Case
• Tests About a Population Mean:
Small-Sample Case
continued
4
Hypothesis Testing
•
•
•
•
Tests About a Population Proportion
Hypothesis Testing and Decision Making
Calculating the Probability of Type II Errors
Determining the Sample Size for a
Hypothesis Test
about a Population Mean
5
A 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  must take one of the following three
forms (where 0 is the hypothesized value of the
population mean).
H0:  > 0
Ha:  < 0
H0:  < 0
Ha:  > 0
H0:  = 0
Ha:   0
6
Type I and Type II Errors
• Since hypothesis tests are based on sample data, we
must allow for the possibility of errors.
• A Type I error is rejecting H0 when it is true.
• A Type II error is accepting H0 when it is false.
• The person conducting the hypothesis test specifies
the maximum allowable probability of making a
Type I error, denoted by  and called the level of
significance.
• Generally, we cannot control for the probability of
making a Type II error, denoted by .
• Statistician avoids the risk of making a Type II error
by using “do not reject H0” and not “accept H0”.
7
Example: Metro EMS
• Type I and Type II Errors
Conclusion
Population Condition
H0 True
Ha True
(  )
( )
Accept H0
(Conclude  
Correct
Conclusion
Reject H0
(Conclude 
Type I
rror
Type II
Error
Correct
Conclusion
8
One-Tailed Tests about a Population Mean:
Large-Sample Case (n > 30)

Hypotheses
H0:   
Ha: 

H0:   
Ha: 
Test Statistic
 Known
z

or
x  0
/ n
 Unknown
z
x  0
s/ n
Rejection Rule
Reject H0 if z > zReject H0 if z < -z
9
Two-Tailed Tests about a Population
Mean:
Large-Sample Case (n > 30)
• Hypotheses
H0:   
Ha:  

 Known
• Test Statistic
x  0
z
/ n
• Rejection Rule
 Unknown
x  0
z
s/ n
Reject H0 if |z| > z
10
Tests about a Population Mean:
Small-Sample Case (n < 30)
• Test Statistic
 Known
x  0
t
/ n
 Unknown
x  0
t
s/ n
This test statistic has a t distribution with n - 1 degrees
of freedom.
• Rejection Rule
One-Tailed
Two-Tailed
H0: 
Reject H0 if t > t
H0: 
Reject H0 if t < -t
H0: 
Reject H0 if |t| > t
11
p -Values and the t
Distribution
• The format of the t distribution table
provided in most statistics textbooks does
not have sufficient detail to determine the
exact p-value for a hypothesis test.
• However, we can still use the t distribution
table to identify a range for the p-value.
• An advantage of computer software
packages is that the computer output will
provide the p-value for the
t distribution.
12
Summary of Test Statistics to be Used in a
Hypothesis Test about a Population Mean
Yes
s known ?
Yes
n > 30 ?
No
Yes
Use s to
estimate s
s known ?
Yes
z
x 
/ n
No
x 
z
s/ n
x 
z
/ n
No
Popul.
approx.
normal
?
No
Use s to
estimate s
x 
t
s/ n
Increase n
to > 30
13
• Selamat Belajar Semoga Sukses.
14