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    Pertemuan 08

    Pengujian Hipotesis 1

    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

    hipotesis untuk suatu dan dua rataan.

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    Outline Materi

    Uji hipotesis nilai tengah Uji hipotesis beda nilai tengah

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    Hypothesis Testing

    Developing Null and Alternative Hypotheses

    Type I and Type II Errors

    One-Tailed Tests About a Population Mean:

    Large-Sample Case

    Two-Tailed Tests About a Population Mean:

    Large-Sample Case

    Tests About a Population Mean:

    Small-Sample Case

    continued

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    Hypothesis Testing

    Tests About a Population Proportion Hypothesis Testing and Decision Making

    Calculating the Probability of Type II

    Errors Determining the Sample Size for a

    Hypothesis Test

    about a Population Mean

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    A Summary of Forms for Null and

    Alternative Hypotheses about a

    Population Mean

    The equality part of the hypotheses always appears in the null

    hypothesis.

    In general, a hypothesis test about the value of a populationmean must take one of the following three forms (where 0

    is the hypothesized value of the population mean).

    H0: > 0 H0:

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    Type I and Type II Errors

    Since hypothesis tests are based on sample data, wemust allow for the possibility of errors.

    A Type I error is rejecting H0when it is true.

    A Type II error is accepting H0when it is false.

    The person conducting the hypothesis test specifiesthe maximum allowable probability of making a

    Type I error, denoted by and called the level ofsignificance.

    Generally, we cannot control for the probability ofmaking a Type II error, denoted by .

    Statistician avoids the risk of making a Type II errorby using do not reject H

    0 and not accept H

    0.

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    Type I and Type II Errors

    Population Condition

    H0 True Ha True

    Conclusion ( < 12 ) ( > 12 )

    Accept H0 Correct Type II(Conclude < 12) Conclusion Error

    Reject H0 Type I Correct(Conclude > 12) rror Conclusion

    Example: Metro EMS

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    s HypothesesHypotheses

    HH00:: 00

    HHaa:: >> 00 HHaa:: > zz RejectReject HH00ififzz < -< -zz

    One-Tailed Tests about a PopulationOne-Tailed Tests about a Population

    Mean: Large-Sample Case (Mean: Large-Sample Case (nn >> 30)30)

    zx

    n=

    0

    /z

    x

    s n=

    0/

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    HypothesesH

    0: =

    0

    H

    a:

    0

    Test Statistic Known Unknown

    Rejection Rule

    Reject H0if |z| > z

    /2

    Two-Tailed Tests about a Population

    Mean:

    Large-Sample Case (n> 30)

    zx

    n

    =

    0

    /z

    x

    s n

    =

    0

    /

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    Test Statistic Known Unknown

    This test statistic has a tdistribution with n - 1 degrees

    of freedom. Rejection Rule

    One-Tailed Two-Tailed H

    0: <

    0Reject H

    0ift> t

    H0: >

    0Reject H

    0ift< -t

    H0: =

    0Reject H

    0if |t| > t

    /2

    Tests about a Population Mean:

    Small-Sample Case (n< 30)

    tx

    n

    =

    0

    /t

    x

    s n

    =

    0

    /

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    p-Values and the t

    Distribution

    The format of the tdistribution table provided inmost statistics textbooks does not have

    sufficient detail to determine the exact p-value

    for a hypothesis test.

    However, we can still use the tdistribution tableto identify a range for thep-value.

    An advantage of computer software packages is

    that the computer output will provide thep-valuefor the

    tdistribution.

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    Summary of Test Statistics to be Used in aSummary of Test Statistics to be Used in a

    Hypothesis Test about a Population MeanHypothesis Test about a Population Mean

    nn >> 30 ?30 ?

    known ?known ?

    Popul.Popul.

    approx.approx.

    normalnormal?? known ?known ?

    UseUse ss totoestimateestimate

    UseUse ss toto

    estimateestimate

    IncreaseIncrease nn

    toto >> 3030/

    xz

    n

    =

    /

    xz

    s n

    =

    /

    xz

    n

    =

    /

    xt

    s n

    =

    YesYes

    YesYes

    YesYes

    YesYes

    NoNo

    NoNo

    NoNo

    NoNo

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    Selamat Belajar Semoga Sukses.

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