Matakuliah
Tahun
: I0134 – Metode Statistika
: 2007
Pertemuan 13
Penarikan Contoh Acak
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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
Sampling Distribution of
x
Sampling Distribution of
p
Properties of Point Estimators
Other Sampling Methods
n = 100
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 as an estimate of a population
parameter.
• We refer to x as the point estimator of the population mean .
• s is the point estimator of the population standard deviation .
• p is the point estimator of the population proportion p.
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Sampling Distribution of
• 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
is the probability
distribution of all possible values of the sample
mean .
• Expected Value of x
E( ) = 
where:
 = the population mean x
x
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Sampling Distribution of

Standard Deviation of
Finite Population
Infinite Population
• 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 x
• If we use a large (n > 30) simple random sample, the central limit
theorem enables us to conclude that the sampling distribution of
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
• Expected Value of
where:
p = the population proportion
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Sampling Distribution of
• Standard Deviation of
Finite Population
p 
–
 pInfinite Population
p(1  p) N  n
n
N 1
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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