Matakuliah
Tahun
: L0104 / Statistika Psikologi
: 2008
Pendugaan Parameter Proporsi dan Varians
(Ragam)
Pertemuan 14
Learning Outcomes
Pada akhir pertemuan ini, diharapkan
mahasiswa akan mampu :
Mahasiswa akan dapat menghitung
pendugaan parameter proporsi satu dan
dua populasi, varians/Ragam dan rasio
dua varians/ragam populasi.
3
Bina Nusantara
Outline Materi
•
•
•
•
Pendugaan proporsi satu populasi
Pendugaan beda dua proporsi
Pendugaan varians satu populasi
Pendugaan rasio dua varians
4
Bina Nusantara
Interval Estimation
of a Population Proportion
• Interval Estimate
p  z / 2
where:
Bina Nusantara
p (1  p )
n
1 -α is the confidence coefficient
zα/2 is the z value providing an area of
cd/2 in the upper tail of the standard
p
normal probability distribution
is the sample proportion
Contoh Soal: Political Science, Inc.
• Interval Estimate of a Population Proportion
p  z / 2
where: n = 500,
p (1  p )
n
p = 220/500 = .44,
z /2 = 1.96
. 44 (1. 44 )
. 44  1. 96
.44 + .0435
500
PSI is 95% confident that the proportion of all voters
that favors the candidate is between .3965 and .4835.
Bina Nusantara
Contoh Soal: Political Science, Inc.
• Sample Size for Interval Estimate of a Population
Proportion
At 99% confidence, z.005 = 2.576.
( z / 2 ) 2 p(1  p) ( 2.576) 2 (. 44)(.56)
n

 1817
2
2
E
(. 03)
Note: We used .44 as the best estimate of p in the
above expression. If no information is available
about p, then .5 is often assumed because it provides
the highest possible sample size. If we had used
p = .5, the recommended n would have been 1843.
Bina Nusantara
Inferences About Population Variances
• Inference about a Population Variance
• Inferences about the Variances of Two
Populations
Bina Nusantara
Inferences About a Population
Variance
• Chi-Square Distribution
• Interval Estimation of σ 2
• Hypothesis Testing
Bina Nusantara
Interval Estimation of σ2
• Interval Estimate of a Population Variance
( n  1) s
2 ( n  1) s
  2
2
 /2
 (1 / 2)
2
2
where the  values are based on a chi-square
distribution with n - 1 degrees of freedom and where
1 - α is the confidence coefficient.
Bina Nusantara
Interval Estimation of σ
• Interval Estimate of a Population Standard
Deviation
Taking the square root of the upper and
lower limits of the variance interval provides the
confidence interval for the population standard
deviation.
Bina Nusantara
Interval Estimation of σ
2
• Chi-Square Distribution With Tail Areas of .025
.025
.025
95% of the
possible 2 values
0
Bina Nusantara
2
.975
2
.025
2
Example: Buyer’s Digest
• Interval Estimation of σ2
n - 1 = 10 - 1 = 9 degrees of freedom and a = .05
2
.975

.025
Bina Nusantara
0

2
.975
(n  1)s 2
2
2
 .025
.025
2
.025
2
Example: Buyer’s Digest
• Interval Estimation of σ2
n - 1 = 10 - 1 = 9 degrees of freedom and a = .05
2.70 
.025
(n  1)s 2
2
2
  .025
Area in
Upper Tail
= .975
2
Bina Nusantara
0 2.70
Example: Buyer’s Digest
• Interval Estimation of σ2
n - 1 = 10 - 1 = 9 degrees of freedom and a = .05
2. 70 
( n  1) s 2
.025

2
 19 . 02
Area in Upper
Tail = .025
2
Bina Nusantara
0 2.70
19.02
Selamat Belajar
Semoga Sukses
Bina Nusantara