1 Pertemuan 06 Sebaran Penarikan Contoh Matakuliah: I0272 – Statistik Probabilitas Tahun: 2005 Versi: Revisi

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menghitungdalil lianit pusat, sebaran X2, t dan F.

3 Outline Materi Sebaran nilai tengah contoh Dalil limit pusat Sebaran Khi-kuadrat Sebaran ragam contoh Sebaran t, standar Sebaran F

4 Sampling and Sampling Distributions Simple Random Sampling Point Estimation Introduction to Sampling Distributions Sampling Distribution of Properties of Point Estimators Other Sampling Methods n = 100 n = 30

5 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.

6 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.

7 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

8 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.

9 Sampling Distribution of Process of Statistical Inference Population Population with mean  = ? Population Population with mean  = ? A simple random sample of n elements is selected from the population. The sample data provide a value for the sample mean. The sample data provide a value for the sample mean. The value of is used to make inferences about the value of . The value of is used to make inferences about the value of .

10 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

11 n Standard Deviation of Finite Population Infinite Population Finite Population Infinite Population A finite population is treated as being infinite if n / N <.05. A finite population is treated as being infinite if n / N <.05. is the finite correction factor. is the finite correction factor. is referred to as the standard error of the mean. is referred to as the standard error of the mean. Sampling Distribution of

12 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. Sampling Distribution of

13 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

14 Sampling Distribution of Standard Deviation of Finite Population Infinite Population – is referred to as the standard error of the proportion.

15 Selamat Belajar Semoga Sukses.