presentasi 03. jarwo

7/29/2019 presentasi 03. Jarwo

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PENGUJIAN HIPOTESIS

STATISTIK: Uji-Z, Uji-t, Uji-F

SUJARWO, SP., MP


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Ingat kembali ruang ruang penerimaan dan

penolakan hipotesis

Two-tailed Test

H0: =

H1:

is divided equally between

the two tails of the criticalregion

Means less than or greater than


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INFERENSI TERHADAP RATA-RATAPOPULASI

Tujuan pengujian untuk mengetahui apakahrata-rata sampel sudah mewakili populasinya.

Ukuran Sampel :

Besar : lebih dari 30 data Uji-Z. Jika Zhit > Ztab

maka Ho ditolak dan Ha di terima, sebaliknya jika

Zhit < Ztab maka Ha ditolak dan Ho diterima

Kecil : Kurang dari 30 data (untuk keperluan praktis). Uji-t .


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Contoh 2: Uji-Z

Rata-rata hasil produksi mesin lama adalah 2200 kg/hari. Sebuah mesin baru diuji dalam 200 hari, ternyatahasil produksinya menyebar secara normal dengan rata-

rata produksi 2280 kg/ hari dan standart deviasi 520 kg/hari. Apakah produktifitas mesin baru lebih baik darimesin lama ?

Hipotesis : H0: = 2200 H1: 2200

Pengujian dilakukan dengan uji Z


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UjiZ Kasus 1:

200520

220022800

/n/

x

hitz

Menghitung Z-Hitung :

Z-hitung = 2,715

Z-tabel = 1,96 - alpha = 0,05 (two tailed)

Karena Z hitung lebih besar dari Z tabel maka Ho di tolak danditerima H1.

Kesimpulan : Produktifitas mesin yang baru lebih tinggi dari yanglama.


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Increasing sample size

S2closer to 2

tstatistic

Critical value of t Depends on sample size

Df

Significant level was chosen byresearcher

Ms

M

n

s

Mt

-5 -4 -3 -2 -1 0 1 2 3 4 5

X

0.0

0.1

0.2

0.3

0.4

Y

-5 -4 -3 -2 -1 0 1 2 3 4 5

X

0.0

0.1

0.2

0.3

0.4

Y

-5 -4 -3 -2 -1 0 1 2 3 4 5

X

0.0

0.1

0.2

0.3

0.4

Y

t-distribution with 2, 5, 10, 30 df

-5 -4 -3 -2 -1 0 1 2 3 4 5

X

0.0

0.1

0.2

0.3

0.4

Y

Uji statistik : Uji-t


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Critical Values of tProportion in one tail 0.25 0.1 0.05 0.025 0.01 0.005Proportion in two tails

df0.5 0.2 0.1 0.05 0.02 0.01

1 1.000 3.078 6.314 12.706 31.821 63.656

2 0.816 1.886 2.920 4.303 6.965 9.925

3 0.765 1.638 2.353 3.182 4.541 5.841

4 0.741 1.533 2.132 2.776 3.747 4.604

5 0.727 1.476 2.015 2.571 3.365 4.032

10 0.700 1.372 1.812 2.228 2.764 3.169

15 0.691 1.341 1.753 2.131 2.602 2.947

20 0.687 1.325 1.725 2.086 2.528 2.845

25 0.684 1.316 1.708 2.060 2.485 2.787

30 0.683 1.310 1.697 2.042 2.457 2.75050 0.679 1.299 1.676 2.009 2.403 2.678

100 0.677 1.290 1.660 1.984 2.364 2.626

1000 0.675 1.282 1.646 1.962 2.330 2.581

1000000 0.674 1.282 1.645 1.960 2.326 2.576


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Hypothesis testing with the t

statistic Basic form

Steps

State H0and H1Set level

Determine critical value of t One or twotailed hypothesis

level

df.

Calculate tvalue

Evaluate H0

errorstandardestimated

Hfrommeanpopulation-datafrommeansample 0t


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Computation

Ms

M

n

s

Mt

11

2

2

2

n

n

XX

n

SSs

1

2

2

2

nn

n

XX

M

n

s

M

s

Mt

M

X 2


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Example 1:

Diketahui produktifitas kedelai di suatu daerahrata-rata adalah 12 kwt/ha. Diambil sampel 15responden. Apakah rerata sampel sama denganpopulasi ?

H0: = 12, H1: 12 = .01, df= 15 - 1 = 14

Critical t(14) = 2.977

Diketahui : Rerata sampel = 11.2

standart deviasi = 3.255

X X2

12 14413 1696 36

11 12112 1448 64

11 121

7 4910 10016 25610 1007 49

14 19615 22516 256

168 2030

X2X


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8406

8733

25583

15

25583.

.

..

n

ssM

95166.8406. 8.8406. 122.11

Ms

Mt

Critical t(14) = 2.977-5 -4 -3 -2 -1 0 1 2 3 4 5

X

0.0

0.1

0.2

0.3

0.4

Y

Gimana kesimpulannya ????


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Example 2:Produktifitas padi rata-ratamenghasilkan 67 kwt/ ha. Dan adateknologi baru dengan data sampelberikut:

H0: = 67, H1: 67

= .05, df= 15 - 1 = 14

Critical t(14) = 2.145

8.7115

1077M

422.477,328.6751,7715

1,159,929751,77

15

107777751

22

2

N

XXSS

X X2

65 422576 577669 476171 504174 547678 608477 592968 462472 5184

75 562574 547664 409669 476163 396982 6724

1077 77751


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30.171115

422.4

1

2

n

SS

s 5.49330.1712 ss

1.418873.3

5.493

15

30.1712

n

ssM

3.38

1.418

8.4

1.418

678.71

Ms

Mt

thit = 3.3845

-5 -4 -3 -2 -1 0 1 2 3 4 5

X

0.0

0.1

0.2

0.3

0.4

Y

Gimana kesimpulannya ????


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Uji Statistik : Uji-F

For cases in which two population variances are to becompared, the F statistic is commonly used.

TestStatistic: F =s1

2/ s22

where s12

and s22

are the sample variances.

The more this ratio deviates from 1, the stronger the evidencefor unequal population variances.

H0: 1 = 2

Ha: 1 2


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The hypothesis that the two standard deviations are equal is

rejected if:


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Example:

Method Mean (ppm)Standard

Deviation (ppm)1 6.7 0.8

2 8.2 1.2

As an example, assume we want to see if a method (Method 1) for measuring

the arsenic concentration in soil is significantly more precisethan a second method (Method 2).Each method was tested ten times, with, yielding the following values:

Since s2 > s1, Fcalc= s22/s1

2 = 1.22/0.82 = 2.25. The tabulated value

for d.o.f. = 9 in each case, and a 1-tailed, 95% confidence level isF9,9 = 3.179. In this case, Fcalc< F9,9, so we accept the nullhypothesis that the two standard deviations are equal, and we are95% confident that any difference in the sample standard deviationsis due to random error. We use a 1-tailed test in this case becausethe only information we are interested in is whether Method 1 ismore precise than Method 2.


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presentasi 03. jarwo

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