8/14/2019 8 pengujian hipotesis 1
1/14
1
Pertemuan 08
Pengujian Hipotesis 1
Matakuliah : I0262 Statistik Probabilitas
Tahun : 2007
Versi : Revisi
8/14/2019 8 pengujian hipotesis 1
2/14
2
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswaakan mampu :
Mahasiswa akan dapat memilih statistik uji
hipotesis untuk suatu dan dua rataan.
8/14/2019 8 pengujian hipotesis 1
3/14
3
Outline Materi
Uji hipotesis nilai tengah Uji hipotesis beda nilai tengah
8/14/2019 8 pengujian hipotesis 1
4/14
4
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
8/14/2019 8 pengujian hipotesis 1
5/14
5
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
8/14/2019 8 pengujian hipotesis 1
6/14
6
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 populationmean must take one of the following three forms (where 0
is the hypothesized value of the population mean).
H0: > 0 H0:
8/14/2019 8 pengujian hipotesis 1
7/14
7
Type I and Type II Errors
Since hypothesis tests are based on sample data, wemust allow for the possibility of errors.
A Type I error is rejecting H0when it is true.
A Type II error is accepting H0when it is false.
The person conducting the hypothesis test specifiesthe maximum allowable probability of making a
Type I error, denoted by and called the level ofsignificance.
Generally, we cannot control for the probability ofmaking a Type II error, denoted by .
Statistician avoids the risk of making a Type II errorby using do not reject H
0 and not accept H
0.
8/14/2019 8 pengujian hipotesis 1
8/14
8
Type I and Type II Errors
Population Condition
H0 True Ha True
Conclusion ( < 12 ) ( > 12 )
Accept H0 Correct Type II(Conclude < 12) Conclusion Error
Reject H0 Type I Correct(Conclude > 12) rror Conclusion
Example: Metro EMS
8/14/2019 8 pengujian hipotesis 1
9/14
9
s HypothesesHypotheses
HH00:: 00
HHaa:: >> 00 HHaa:: > zz RejectReject HH00ififzz < -< -zz
One-Tailed Tests about a PopulationOne-Tailed Tests about a Population
Mean: Large-Sample Case (Mean: Large-Sample Case (nn >> 30)30)
zx
n=
0
/z
x
s n=
0/
8/14/2019 8 pengujian hipotesis 1
10/14
10
HypothesesH
0: =
0
H
a:
0
Test Statistic Known Unknown
Rejection Rule
Reject H0if |z| > z
/2
Two-Tailed Tests about a Population
Mean:
Large-Sample Case (n> 30)
zx
n
=
0
/z
x
s n
=
0
/
8/14/2019 8 pengujian hipotesis 1
11/14
11
Test Statistic Known Unknown
This test statistic has a tdistribution with n - 1 degrees
of freedom. Rejection Rule
One-Tailed Two-Tailed H
0: <
0Reject H
0ift> t
H0: >
0Reject H
0ift< -t
H0: =
0Reject H
0if |t| > t
/2
Tests about a Population Mean:
Small-Sample Case (n< 30)
tx
n
=
0
/t
x
s n
=
0
/
8/14/2019 8 pengujian hipotesis 1
12/14
12
p-Values and the t
Distribution
The format of the tdistribution table provided inmost statistics textbooks does not have
sufficient detail to determine the exact p-value
for a hypothesis test.
However, we can still use the tdistribution tableto identify a range for thep-value.
An advantage of computer software packages is
that the computer output will provide thep-valuefor the
tdistribution.
8/14/2019 8 pengujian hipotesis 1
13/14
13
Summary of Test Statistics to be Used in aSummary of Test Statistics to be Used in a
Hypothesis Test about a Population MeanHypothesis Test about a Population Mean
nn >> 30 ?30 ?
known ?known ?
Popul.Popul.
approx.approx.
normalnormal?? known ?known ?
UseUse ss totoestimateestimate
UseUse ss toto
estimateestimate
IncreaseIncrease nn
toto >> 3030/
xz
n
=
/
xz
s n
=
/
xz
n
=
/
xt
s n
=
YesYes
YesYes
YesYes
YesYes
NoNo
NoNo
NoNo
NoNo
8/14/2019 8 pengujian hipotesis 1
14/14
14
Selamat Belajar Semoga Sukses.
Top Related