soal uts statistika lingkungan psl 2009

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Nama : __________________________

NRP : __________________________ S2/S3

UJIAN TENGAH SEMESTER (UTS)STATISTIKA LINGKUNGAN

Rabu, 12 November 2009, pkl. 09.00-11.00Catatan Terbuka

1. Pada penarikan contoh acak berpeluang (probability sampling) dikenal beberapa teknik penarikan contoh, antara lain penarikan contoh acak sederhana (simple random sampling), penarikan contoh acak berlapis (stratified random sampling), penarikan contoh acak gerombol (cluster random sampling) dan penarikan contoh acak sistematis (systematic random sampling). Jelaskan pada kondisi apa masing-masing teknik tersebut digunakan dan bagaimana prosedur penarikan contohnya?

penarikan contoh acak sederhana (simple random sampling) :

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penarikan contoh acak berlapis (stratified random sampling) :

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penarikan contoh acak gerombol (cluster random sampling) :

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penarikan contoh acak sistematis (systematic random sampling) :

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2. Misalkan Saudara diminta untuk melakukan penelitian mengenai manfaat program pemberdayaan masyarakt yang dilakukan oleh pemerintah dalam upaya meningkatkan taraf hidup masyarakat di sekitar hutan lindung di daerah terpencil dan Saudara tidak mendapatkan data yang akan digunakan sebagai kerangka percontohan (sampling frame), teknik penarikan contoh berpeluang apa yang akan Saudara gunakan dan bagaimana prosedurnya? ________________________________________________________________________

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Jika ternyata juga Saudara tidak mendapatkan data taraf hidup masyarakat sebelum adanya program pemerintah tersebut, dengan cara apa Saudara dapat membandingkan manfaat adanya program tersebut bagi taraf hidup masyarakat dibanding sebelumnya ?________________________________________________________________________

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3. Seorang pengusaha agrobisnis memiliki 3 varietas kentang yang ditanam pada 4 lokasi yang berbeda. Untuk mengetahui apakah ada perbedaan pengaruh varietas maupun lokasi terhadap hasil produksi kentangnya, ia mengambil masing-masing 3 sampel dari setiap kombinasi varietas-lokasi kemudian diukur beratnya. a. Tuliskan model linear beserta keterangannya

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b. Tuliskan semua hipotesisnya

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_____________________________________________________________________c. Hasil Analisis Ragam dari penelitian tersebut disajikan pada Tabel ANOVA berikut. Lengkapilah. Two-way ANOVA: Hasil versus Lokasi, Varietas

Source DF SS MS F P

Lokasi 468.22 0.000

Varietas 98.111 0.001

Interaction 78.44 0.331

Error

Total 1000.22

S = R-Sq = % d. Berdasarkan output Minitab pada bagian c., apa kesimpulan Saudara berkaitan dengan hipotesis yang Saudara buat pada bagian b.?_____________________________________________________________________

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_____________________________________________________________________4. Untuk meneliti hubungan antara jarak (km) yang ditempuh sebuah mobil dengan emisi (ppm) hydrocarbon yang dihasilkan, diambil contoh 10 mobil dan dengan menggunakan Analisis Regresi Linear Sederhana diperoleh output sebagai berikut :

Predictor Coef SE Coef T P

Constant 381.95 42.40 9.01 0.000

Jarak 5.3893 0.6233 8.65 0.000

Analysis of Variance

Source DF SS MS F P

Regression 1 131932 131932 74.76 0.000

Residual Error 8 14118 1765

Total 9 146051

a. Tentukan persamaan regresinya dan interpretasikan masing-masing koefisiennya_____________________________________________________________________

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_____________________________________________________________________b. Tentukan koefisien determinasinya dan interpretasikan_____________________________________________________________________

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5. Sebuah penelitian ingin mengetahui hubungan antara peubah respon Y dengan 3 peubah penjelas X1, X2, X3. Untuk itu diambil contoh sebanyak 16 dan dianalisis menggunakan Analisis Regresi Berganda. Hasilnya dapat dilihat dari output berikut.

Regression Analysis: Y versus X1, X2, X3

Predictor Coef SE Coef T P

Constant 965.3 499.8 1.93 0.077

X1 2.865 1.583 1.81 0.095

X2 6.75 10.28 0.66 0.524

X3 0.2873 0.1111 2.59 0.024

S = 1008.96 R-Sq = 78.8% R-Sq(adj) = 73.5%

Analysis of Variance

Source DF SS MS F P

Regression 3 45510101 15170034 14.90 0.000

Residual Error 12 12215892 1017991

Total 15 57725994

a. Tuliskan persamaan regresinya__________________________________________________________________

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b. Tentukan besarnya koefisien determinasinya dan interpretasikan.

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c. Ujilah dengan menggunakan uji-t apakah X1 berpengaruh secara signifikan terhadap Y, lakukan hal yang sama untuk X2 dan X3.__________________________________________________________________

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d. Jika kita menginginkan untuk memilih model terbaik yang melibatkan X1, X2 dan/atau X3, dan diberikan output minitab berikut, model mana yang akan Saudara pilih? Jelaskan alasan Saudara.__________________________________________________________________

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Model 1 :

Regression Analysis: Y versus X1, X2, X3

The regression equation is

Y = 965 + 2.87 X1 + 6.8 X2 + 0.287 X3

Predictor Coef SE Coef T P VIF

Constant 965.3 499.8 1.93 0.077

X1 2.865 1.583 1.81 0.095 2.3

X2 6.75 10.28 0.66 0.524 1.9

X3 0.2873 0.1111 2.59 0.024 2.2

S = 1008.96 R-Sq = 78.8% R-Sq(adj) = 73.5%

Analysis of Variance

Source DF SS MS F P

Regression 3 45510101 15170034 14.90 0.000

Residual Error 12 12215892 1017991

Total 15 57725994

Model 2 :

Regression Analysis: Y versus X1, X3

The regression equation is

Y = 1135 + 3.26 X1 + 0.310 X3

Predictor Coef SE Coef T P VIF

Constant 1134.8 418.6 2.71 0.018

X1 3.258 1.434 2.27 0.041 2.0

X3 0.3099 0.1033 3.00 0.010 2.0

S = 986.655 R-Sq = 78.1% R-Sq(adj) = 74.7%

Analysis of Variance

Source DF SS MS F P

Regression 2 45070638 22535319 23.15 0.000

Residual Error 13 12655356 973489

Total 15 57725994

Model 3 :

Regression Analysis: Y versus X2, X3

The regression equation is

Y = 1198 + 13.8 X2 + 0.387 X3

Predictor Coef SE Coef T P VIF

Constant 1197.6 523.6 2.29 0.040

X2 13.77 10.32 1.33 0.205 1.6

X3 0.3874 0.1044 3.71 0.003 1.6

S = 1093.75 R-Sq = 73.1% R-Sq(adj) = 68.9%

Analysis of Variance

Source DF SS MS F P

Regression 2 42174166 21087083 17.63 0.000

Residual Error 13 15551828 1196294

Total 15 57725994

Best Subsets Regression: Y versus X1, X2, X3

Response is Y

Mallows X X X

Vars R-Sq R-Sq(adj) C-p S 1 2 3

1 69.4 67.2 5.4 1123.8 X

1 62.9 60.2 9.0 1237.0 X

2 78.1 74.7 2.4 986.66 X X

2 73.1 68.9 5.3 1093.8 X X

3 78.8 73.5 4.0 1009.0 X X X

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