PENDUGAAN PARAMETER Pertemuan 8

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2 PENDUGAAN PARAMETER Pertemuan 8
Matakuliah : I STATISTIK PROBABILITAS Tahun : 2009 PENDUGAAN PARAMETER Pertemuan 8

3 Materi Pendugaan parameter proporsi (pendugaan titik dan selang)
Pendugaan parameter ragam (pendugaan titik dan selang) Bina Nusantara University

4 Estimasi Interval 1 Proporsi Populasi
Selang kepercayaan bagi p untuk contoh berukuran besar : Bila adalah proporsi keberhasilan dalam suatu contoh acak berukuran n, dan = ,maka selang kepercayaan (1 - )100% bagi p adalah: Bina Nusantara University 4

5 Estimasi Beda 2 Proporsi
Selang kepercayaan bagi p1 – p2 untuk contoh berukuran besar: Bila masing-2 adalah proporsi keberhasilan dalam contoh acak berukuran n1 dan n2, serta , maka selang kepercayaan (1 - ) 100% bagi p1 – p2 adalah : Bina Nusantara University

6 Inferences About Population Variances
Inference about a Population Variance Inferences about the Variances of Two Populations Chi-Square Distribution Interval Estimation of 2 Bina Nusantara University 6 6

7 Chi-Square Distribution
We will use the notation to denote the value for the chi-square distribution that provides an area of a to the right of the stated value. For example, there is a .95 probability of obtaining a c2 (chi-square) value such that Bina Nusantara University

8 Interval Estimation of 2
95% of the possible 2 values .025 .025 2 Bina Nusantara University

9 Interval Estimation of 2
There is a (1 – a) probability of obtaining a c2 value such that Substituting (n – 1)s2/s 2 for the c2 we get Performing algebraic manipulation we get Bina Nusantara University

10 Interval Estimation of 2
Interval Estimate of a Population Variance where the values are based on a chi-square distribution with n - 1 degrees of freedom and where 1 -  is the confidence coefficient. Bina Nusantara University

11 Interval Estimation of 
Interval Estimate of a Population Standard Deviation Taking the square root of the upper and lower limits of the variance interval provides the confidence interval for the population standard deviation. Bina Nusantara University

12 Interval Estimation of 2
Example: Buyer’s Digest (A) Buyer’s Digest rates thermostats manufactured for home temperature control. In a recent test, 10 thermostats manufactured by ThermoRite were selected and placed in a test room that was maintained at a temperature of 68oF. The temperature readings of the ten thermostats are shown on the next slide. Bina Nusantara University

13 Interval Estimation of 2
Example: Buyer’s Digest (A) We will use the 10 readings below to develop a 95% confidence interval estimate of the population variance. Thermostat Temperature Bina Nusantara University

14 For n - 1 = = 9 d.f. and a = .05 Selected Values from the Chi-Square Distribution Table Our value Bina Nusantara University

15 For n - 1 = 10 - 1 = 9 d.f. and a = .05 .025 Area in Upper Tail = .975
2 2.700 Bina Nusantara University

16 Interval Estimation of 2 For n - 1 = 10 - 1 = 9 d.f. and a = .05
Selected Values from the Chi-Square Distribution Table Bina Nusantara University Our value

17 Interval Estimation of 2
n - 1 = = 9 degrees of freedom and a = .05 .025 Area in Upper Tail = .025 2 2.700 19.023 Bina Nusantara University

18 Interval Estimation of 2
Sample variance s2 provides a point estimate of  2. A 95% confidence interval for the population variance is given by: .33 < 2 < 2.33 Bina Nusantara University

19 Pendugaan Rasio Dua Varians
Selang kepercayaan bagi Bila S12 dan S22 adalah ragam dua contoh bebas berukuran n1 dan n2 yang diambil dari populasi normal, maka selang kepercayaan (1 - ) 100% bagi . Bina Nusantara University 19