1

Pertemuan 09Pengujian Hipotesis 2

Matakuliah : I0272 – Statistik Probabilitas

Tahun : 2005

Versi : Revisi

2

Learning Outcomes

Pada akhir pertemuan ini, diharapkan mahasiswa

akan mampu :

• Mahasiswa akan dapat memilih statistik uji proporsi, ragam dan uji kebaikan suai.

3

Outline Materi

• Uji hipotesis proporsi

• Uji hipotesis ragam

• Uji kebaikan suai

4

A Summary of Forms for Null and Alternative Hypotheses about a Population Proportion

• The equality part of the hypotheses always appears in the null hypothesis.

• In general, a hypothesis test about the value of a population proportion p must take one of the following three forms (where p0 is the hypothesized value of the population proportion).

H0: p > p0 H0: p < p0 H0: p = p0

Ha: p < p0 Ha: p > p0 Ha: p p0

5

Tests about a Population Proportion: Large-Sample Case (np > 5 and n(1 - p)

> 5)

• Test Statistic

where:

• Rejection Rule

One-Tailed Two-Tailed

H0: pp Reject H0 if z > z

H0: pp Reject H0 if z < -z

H0: pp Reject H0 if |z| > z

zp p

p

0

z

p p

p

0

pp p

n

0 01( ) pp p

n

0 01( )

6

Example: NSC

• Two-Tailed Test about a Population Proportion: Large n– Hypothesis H0: p = .5

Ha: p .5

– Test Statistic

0 (67/ 120) .51.278

.045644p

p pz

0 (67/ 120) .51.278

.045644p

p pz

0 0(1 ) .5(1 .5).045644

120p

p pn

0 0(1 ) .5(1 .5).045644

120p

p pn

7

Contoh Soal: NSC

• Two-Tailed Test about a Population Proportion: Large n– Rejection Rule

Reject H0 if z < -1.96 or z > 1.96

– Conclusion

Do not reject H0.

For z = 1.278, the p-value is .201. If we reject

H0, we exceed the maximum allowed risk of committing a Type I error (p-value > .050).

8

Tests of Goodness of Fit and Independence

• Goodness of Fit Test: A Multinomial Population

• Tests of Independence: Contingency Tables

• Goodness of Fit Test: Poisson and Normal Distributions

9

Goodness of Fit Test:A Multinomial Population

1. Set up the null and alternative hypotheses.

2. Select a random sample and record the

observed

frequency, fi , for each of the k categories.

3. Assuming H0 is true, compute the expected

frequency, ei , in each category by

multiplying the category probability by the

sample size.

continued

10

Goodness of Fit Test:A Multinomial Population

4. Compute the value of the test statistic.

5. Reject H0 if

(where is the significance level and there are k - 1 degrees of freedom).

22

1

( )f ee

i i

ii

k2

2

1

( )f ee

i i

ii

k

2 2 2 2

11

Contoh Soal: Finger Lakes Homes

•Multinomial Distribution Goodness of Fit Test

The number of homes sold of each model for 100

sales over the past two years is shown below.

Model Colonial Ranch Split-Level A-Frame

# Sold 30 20 35 15

12

• Selamat Belajar Semoga Sukses.