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    Pertemuan 09

    Pengujian Hipotesis 2

    Matakuliah : I0262 Statistik Probabilitas

    Tahun : 2007

    Versi : Revisi

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    Learning Outcomes

    Pada akhir pertemuan ini, diharapkan mahasiswaakan mampu :

    Mahasiswa akan dapat memilih statistik uji

    proporsi, ragam dan uji kebaikan suai.

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    Outline Materi

    Uji hipotesis proporsi Uji hipotesis ragam

    Uji kebaikan suai

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    A Summary of Forms for Null and Alternative

    Hypotheses about a Population Proportion

    The equality part of the hypotheses alwaysappears in the null hypothesis.

    In general, a hypothesis test about the value of a

    population proportionpmust take one of the

    following three forms (wherep0 is the

    hypothesized value of the population proportion).

    H0: p >p0 H0: p

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    Tests about a Population Proportion:

    Large-Sample Case (np> 5 and n(1 - p)

    > 5)

    Test Statistic

    where:

    Rejection Rule

    One-Tailed Two-Tailed H

    0

    : p < p0

    Reject H0

    if z > z

    H0: p > p

    0Reject H

    0if z < -z

    H0: p = p

    0Reject H

    0if |z| > z

    /2

    zp p

    p

    =

    0

    pp p

    n=

    0 01( )

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    Example: NSC

    Two-Tailed Test about a PopulationProportion: Large n

    Hypothesis H0: p = .5

    Ha:p .5 Test Statistic

    0 (67/ 120) .5 1.278.045644

    p

    p pz

    = = =

    0 0(1 ) .5(1 .5) .045644120

    p

    p p

    n

    = = =

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    Contoh Soal: NSC

    Two-Tailed Test about a Population Proportion: Large n

    Rejection Rule

    Reject H0 ifz< -1.96 orz> 1.96

    Conclusion

    Do not reject H0.

    Forz= 1.278, thep-value is .201. If we reject

    H0, we exceed the maximum allowed risk of

    committing a Type I error (p-value > .050).

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    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

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    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 thesample size.

    continued

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    Goodness of Fit Test:

    A Multinomial Population

    4. Compute the value of the test statistic.

    5. Reject H0 if

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

    2 2

    1

    = =

    ( )f e

    ei i

    ii

    k

    2 2

    1

    = =

    ( )f ee

    i i

    ii

    k

    2 2>

    2 2>

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    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

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    Selamat Belajar Semoga Sukses.