Matakuliah
Tahun
Versi
: I0262 – Statistik Probabilitas
: 2007
: Revisi
Pertemuan 06
Sebaran Penarikan Contoh
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa akan dapat menghitungdalil
lianit pusat, sebaran X2, t dan F.
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Outline Materi
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Sebaran nilai tengah contoh
Dalil limit pusat
Sebaran Khi-kuadrat
Sebaran ragam contoh
Sebaran t, standar
Sebaran F
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Sampling and Sampling
Distributions
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Simple Random Sampling
Point Estimation
Introduction to Sampling Distributions
n = 100
Sampling Distribution of x
Sampling Distribution of p
Properties of Point Estimators
Other Sampling Methods
n = 30
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Statistical Inference
• The purpose of statistical inference is to
obtain information about a population from
information contained in a sample.
• A population is the set of all the elements of
interest.
• A sample is a subset of the population.
• The sample results provide only estimates of
the values of the population characteristics.
• A parameter is a numerical characteristic of a
population.
• With proper sampling methods, the sample
results will provide “good” estimates of the
population characteristics.
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Simple Random Sampling
• Finite Population
– Replacing each sampled element before selecting
subsequent elements is called sampling with
replacement.
– A simple random sample from a finite population
of size N is a sample selected such that each
possible sample of size n has the same probability
of being selected.
– Sampling without replacement is the procedure
used most often.
– In large sampling projects, computer-generated
random numbers are often used to automate the
sample selection process.
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Simple Random Sampling
• Infinite Population
– A simple random sample from an infinite
population is a sample selected such that the
following conditions are satisfied.
• Each element selected comes from the same
population.
• Each element is selected independently.
– The population is usually considered infinite if it
involves an ongoing process that makes listing or
counting every element impossible.
– The random number selection procedure cannot
be used for infinite populations.
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Point Estimation
• In point estimation we use the data from the
sample to compute a value of a sample statistic
that serves xas an estimate of a population
parameter.
• We refer to as the point estimator of the
population mean .
p the point estimator of the population
• s is
standard deviation .
•
is the point estimator of the population
proportion p.
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Sampling Distribution of
x
• Process of Statistical Inference
Population
with mean
=?
The value of x is used to
make inferences about
the value of .
A simple random sample
of n elements is selected
from the population.
The sample data
provide a value for
the sample mean x.
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Sampling Distribution of
x
• The sampling distribution of x is the
probability distribution of all possible
values of the sample
mean .
• Expected Value of x
E( x ) = 
where:
 = the population mean
x
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Sampling Distribution of

Standard Deviation of
x x
Finite Population

N n
x  ( )
n N 1
Infinite Population
x 

n
• A finite population is treated as being infinite if
n/N < .05.
• ( N  n) / ( N  1) is the finite correction factor.
•  x is referred to as the standard error of the mean.
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Sampling Distribution of
• If we use a large (n > 30) simple random
sample, the central limit theorem enables us to
conclude that the sampling distribution of x can
be approximated by a normal probability
distribution.
• When the simple random sample is small (n <
30), the sampling distribution of x can be
considered normal only if we assume the
population has a normal probability distribution.
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Sampling Distribution of
• The sampling distribution of p is the
probability distribution of all possible
values of the sample proportion
E ( p)  p
• Expected Value of p
where:
p = the population proportion
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Sampling Distribution of
p
• Standard Deviation of p
Finite Population
 p p
–
p(1  p) N  n
n
N 1
Infinite Population
p 
p(1  p)
n
is referred to as the standard error of
the proportion.
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• Selamat Belajar Semoga Sukses.
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