PENDUGAAN PARAMETER Pertemuan 7 Matakuliah : I0272 - STATISTIK PROBABILITAS Tahun : 2009 PENDUGAAN PARAMETER Pertemuan 7

Materi Pendugaan Titik dan Selang Pendugaan Selang: Nilai tengah dan beda dua nilai tengah Bina Nusantara University

Pendugaan Titik dan Selang Pendugaan Parameter. Suatu statistik merupakan nilai dugaan bagi parameter populasi . Misalnya merupakan nilai dugaan bagi , penduga ini disebut Penduga Titik. Definisi : Suatu statistik disebut penduga tak bias bagi parameter  bila  = E() =  Penduga yang lebih baik: Dugaan Selang. Secara umum: dugaan selang bagi parameter populasi  adalah suatu yang berbentuk Bina Nusantara University

Pendugaan Selang: Nilai tengah dan beda 2 nilai tengah Interval Estimation of a Population Mean: 1 populasi Large-Sample Case (n > 30) Small-Sample Case (n < 30) Interval Estimation of a Population Mean: 2 populasi  [--------------------- ---------------------] [--------------------- ---------------------] [--------------------- ---------------------] Bina Nusantara University 5

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 s is the population standard deviation n is the sample size Bina Nusantara University 6

Small-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. Small-Sample Case (n < 30) with  Unknown Interval Estimate: Bina Nusantara University 7

Interval Estimation of a Population Mean: Small-Sample Case (n < 30) Population is Not Normally Distributed. The only option is to increase the sample size to n > 30 and use the large-sample interval-estimation procedures. Population is Normally Distributed and  is Known. The large-sample interval-estimation procedure can be used. Population is Normally Distributed and  is Unknown. The appropriate interval estimate is based on a probability distribution known as the t distribution. Bina Nusantara University 8

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 Bina Nusantara University 9

Interval Estimate of 1 - 2: Large-Sample Case (n1 > 30 and n2 > 30) Interval Estimate with 1 and 2 Known where: 1 -  is the confidence coefficient Interval Estimate with 1 and 2 Unknown Bina Nusantara University 10

Interval Estimate of 1 - 2: Small-Sample Case (n1 < 30 and/or n2 < 30) Interval Estimate with  2 Known where: Bina Nusantara University 11

Interval Estimate of 1 - 2: Small-Sample Case (n1 < 30 and/or n2 < 30) Interval Estimate with  2 Unknown where: Bina Nusantara University 12

Contoh Soal: Specific Motors Point Estimate of the Difference Between 2 Population Means 1 = mean miles-per-gallon for the population of M cars 2 = mean miles-per-gallon for the population of J cars Point estimate of 1 - 2 = = 29.8 - 27.3 = 2.5 mpg. Bina Nusantara University 13

Contoh Soal: Specific Motors 95% Confidence Interval Estimate of the Difference Between Two Population Means: Small-Sample Case = 2.5 + 2.2 or .3 to 4.7 miles per gallon. We are 95% confident that the difference between the mean mpg ratings of the two car types is from .3 to 4.7 mpg (with the M car having the higher mpg). Bina Nusantara University 14