1. 1 Pertemuan 07 Pendugaan Parameter Matakuliah: I0262 – Statistik Probabilitas Tahun: 2007 Versi: Revisi

2. 2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menghasilkan dugaan parameter, nilai tengah, proporsi dan ragam.

3. 3 Outline Materi Pendugaan Titik Pendugaan Selang : nilai tengah, proporsi dan ragam.

4. 4 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.

5. 5 Sampling Error The absolute difference between an unbiased point estimate and the corresponding population parameter is called the sampling error. Sampling error is the result of using a subset of the population (the sample), and not the entire population to develop estimates. The sampling errors are: for sample mean | s -  for sample standard deviation for sample proportion

6. 6 [--------------------- ---------------------]  Interval Estimation Interval Estimation of a Population Mean: Large-Sample Case Interval Estimation of a Population Mean: Small-Sample Case Determining the Sample Size Interval Estimation of a Population Proportion

7. 7 Interval Estimate of a Population Mean: Large-Sample Case (n > 30) With  Known where: is the sample mean 1 -  is the confidence coefficient z  /2 is the z value providing an area of  /2 in the upper tail of the standard normal probability distribution  is the population standard deviation n is the sample size

8. 8 Interval Estimate of a Population Mean: Large-Sample Case (n > 30) With  Unknown In most applications the value of the population standard deviation is unknown. We simply use the value of the sample standard deviation, s, as the point estimate of the population standard deviation.

9. 9 Interval Estimation of a Population Mean: Small-Sample Case (n < 30) with  Unknown Interval Estimate where 1 -  = the confidence coefficient t  /2 = the t value providing an area of  /2 in the upper tail of a t distribution with n - 1 degrees of freedom s = the sample standard deviation

10. 10 Interval Estimation of a Population Proportion Interval Estimate where: 1 -  is the confidence coefficient z  /2 is the z value providing an area of  /2 in the upper tail of the standard normal probability distribution is the sample proportion

11. 11 Point Estimator of the Difference Between the Means of Two Populations Let  1 equal the mean of population 1 and  2 equal the mean of population 2. The difference between the two population means is  1 -  2. To estimate  1 -  2, we will select a simple random sample of size n 1 from population 1 and a simple random sample of size n 2 from population 2. Let equal the mean of sample 1 and equal the mean of sample 2. The point estimator of the difference between the means of the populations 1 and 2 is.

12. 12 Interval Estimate with  1 and  2 Known where: 1 -  is the confidence coefficient Interval Estimate with  1 and  2 Unknown where: Interval Estimate of  1 -  2 : Large-Sample Case (n 1 > 30 and n 2 > 30)

13. 13 Interval Estimate of  1 -  2 : Small-Sample Case (n 1 < 30 and/or n 2 < 30) Interval Estimate with  2 Known where:

14. 14 Interval Estimate of  1 -  2 : Small-Sample Case (n 1 < 30 and/or n 2 < 30) Interval Estimate with  2 Unknown where:

15. 15 Selamat Belajar Semoga Sukses.