Matakuliah
Tahun
Versi
: I0262 – Statistik Probabilitas
: 2007
: Revisi
Pertemuan 09
Pengujian Hipotesis 2
1
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat memilih statistik uji
proporsi, ragam dan uji kebaikan suai.
2
Outline Materi
• Uji hipotesis proporsi
• Uji hipotesis ragam
• Uji kebaikan suai
3
A Summary of Forms for Null and Alternative
Hypotheses about a Population Proportion
• The equality part of the hypotheses always
appears in the null hypothesis.
• In general, a hypothesis test about the value of a
population proportion p must take one of the
following three forms (where p0 is the
hypothesized value of the population proportion).
H0: p > p0
Ha: p < p0
H0: p < p0
Ha: p > p0
H0: p = p0
Ha: p  p0
4
Tests about a Population Proportion:
Large-Sample Case (np > 5 and n(1 p) > 5)
• Test Statistic
where:
z
p 
• Rejection Rule
H0: p  p
H0: p  p
H0: pp
p  p0
p
p0 (1  p0 )
n
One-Tailed
Reject H0 if z > z
Reject H0 if z < -z
Two-Tailed
Reject H0 if |z| > z
5
Example: NSC
• Two-Tailed Test about a Population
Proportion: Large n
– Hypothesis
H0: p = .5
Ha: p  .5
– Test Statistic
p0 (1  p0 )
.5(1  .5)
p 

 .045644
n
120
z
p  p0
p

(67 /120)  .5
 1.278
.045644
6
Contoh Soal: NSC
• Two-Tailed Test about a Population Proportion:
Large n
– Rejection Rule
Reject H0 if z < -1.96 or z > 1.96
– Conclusion
Do not reject H0.
For z = 1.278, the p-value is .201. If we
reject
H0, we exceed the maximum allowed risk of
committing a Type I error (p-value > .050).
7
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
8
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 the
sample size.
continued
9
Goodness of Fit Test:
A Multinomial Population
4. Compute the value of the test statistic.
( f ii  eii ) 22
 
eii
ii11
22
kk
 2   2
5. Reject H0 if
(where  is the significance level and
there are k - 1 degrees of freedom).
10
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
Frame
# Sold
15
Colonial
30
Ranch
20
Split-Level A35
11
• Selamat Belajar Semoga Sukses.
12