9 pengujian hipotesis 2
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Pertemuan 09
Pengujian Hipotesis 2
Matakuliah : I0262 Statistik Probabilitas
Tahun : 2007
Versi : Revisi
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswaakan mampu :
Mahasiswa akan dapat memilih statistik uji
proporsi, ragam dan uji kebaikan suai.
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Outline Materi
Uji hipotesis proporsi Uji hipotesis ragam
Uji kebaikan suai
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A Summary of Forms for Null and Alternative
Hypotheses about a Population Proportion
The equality part of the hypotheses alwaysappears in the null hypothesis.
In general, a hypothesis test about the value of a
population proportionpmust take one of the
following three forms (wherep0 is the
hypothesized value of the population proportion).
H0: p >p0 H0: p
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Tests about a Population Proportion:
Large-Sample Case (np> 5 and n(1 - p)
> 5)
Test Statistic
where:
Rejection Rule
One-Tailed Two-Tailed H
0
: p < p0
Reject H0
if z > z
H0: p > p
0Reject H
0if z < -z
H0: p = p
0Reject H
0if |z| > z
/2
zp p
p
=
0
pp p
n=
0 01( )
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Example: NSC
Two-Tailed Test about a PopulationProportion: Large n
Hypothesis H0: p = .5
Ha:p .5 Test Statistic
0 (67/ 120) .5 1.278.045644
p
p pz
= = =
0 0(1 ) .5(1 .5) .045644120
p
p p
n
= = =
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Contoh Soal: NSC
Two-Tailed Test about a Population Proportion: Large n
Rejection Rule
Reject H0 ifz< -1.96 orz> 1.96
Conclusion
Do not reject H0.
Forz= 1.278, thep-value is .201. If we reject
H0, we exceed the maximum allowed risk of
committing a Type I error (p-value > .050).
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Tests of Goodness of Fit and
Independence
Goodness of Fit Test: A Multinomial
Population
Tests of Independence: Contingency
Tables
Goodness of Fit Test: Poisson and
Normal Distributions
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Goodness of Fit Test:
A Multinomial Population
1. Set up the null and alternative hypotheses.
2. Select a random sample and record the
observed
frequency, fi, for each of the k categories.
3. Assuming H0 is true, compute the expected
frequency, ei, in each category by
multiplying the category probability by thesample size.
continued
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Goodness of Fit Test:
A Multinomial Population
4. Compute the value of the test statistic.
5. Reject H0 if
(where is the significance level andthere are k- 1 degrees of freedom).
2 2
1
= =
( )f e
ei i
ii
k
2 2
1
= =
( )f ee
i i
ii
k
2 2>
2 2>
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Contoh Soal: Finger Lakes
Homes
Multinomial Distribution Goodness of Fit Test
The number of homes sold of each model for 100
sales over the past two years is shown below.
Model Colonial Ranch Split-Level A-Frame
# Sold 30 20 35 15
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Selamat Belajar Semoga Sukses.