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Pertemuan 06Sebaran Penarikan Contoh

Matakuliah : I0262 – Statistik Probabilitas

Tahun : 2007

Versi : Revisi

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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

• 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

• Simple Random Sampling• Point Estimation• Introduction to Sampling Distributions• Sampling Distribution of • Sampling Distribution of• Properties of Point Estimators• Other Sampling Methods

xx

pp

nn = 100 = 100

nn = 30 = 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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• 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.

Simple Random Sampling

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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 as the point estimator of the population mean .

• s is the point estimator of the population standard deviation .

• is the point estimator of the population proportion p.

xx

pp

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Sampling Distribution of

• Process of Statistical Inference

Population Population with meanwith mean

= ?= ?

Population Population with meanwith mean

= ?= ?

A simple random sampleA simple random sampleof of nn elements is selected elements is selected

from the population.from the population.

xx

The sample data The sample data provide a value forprovide a value for

the sample meanthe sample mean . .

The sample data The sample data provide a value forprovide a value for

the sample meanthe sample mean . .xx

The value of is used toThe value of is used tomake inferences aboutmake inferences about

the value of the value of ..

The value of is used toThe value of is used tomake inferences aboutmake inferences about

the value of the value of ..

xx

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• The sampling distribution of is the probability distribution of all possible values of the sample

mean .

• Expected Value of

E( ) = where:

= the population mean

Sampling Distribution of xx

xx

xxxxxx

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Standard Deviation ofStandard Deviation of

Finite PopulationFinite Population Infinite Infinite Population Population

• A finite population is treated as being A finite population is treated as being infinite if infinite if nn//NN << .05. .05.

• is the finite correction is the finite correction factor.factor.

• is referred to as the is referred to as the standard error of the standard error of the meanmean..

xx

x n

N nN

( )1

x n

N nN

( )1

x n

x n

( ) / ( )N n N 1( ) / ( )N n N 1

x x

Sampling Distribution of

xx

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• 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 can be considered normal only if we assume the population has a normal probability distribution.

xx

xx

Sampling Distribution of

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• The sampling distribution of is the probability distribution of all possible values of the sample proportion

• Expected Value of

where:

p = the population proportion

Sampling Distribution of

pp

pp

E p p( ) E p p( )

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Sampling Distribution of pp

pp

pp pn

N nN

( )11

pp pn

N nN

( )11

pp pn

( )1 pp pn

( )1 p p

• Standard Deviation of

Finite Population Infinite Population

– is referred to as the standard error of the proportion.

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• Selamat Belajar Semoga Sukses.