Pertemuan 16 pendugaan parameter
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Pertemuan 16 Pendugaan Parameter. Matakuliah: I0134 – Metoda Statistika Tahun: 2005 Versi: Revisi. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa dapat menghitung penduga selang dari rataan, proporsi dan varians. Outline Materi.

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Pertemuan 16 Pendugaan Parameter

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Pertemuan 16 pendugaan parameter

Pertemuan 16Pendugaan Parameter

Matakuliah: I0134 – Metoda Statistika

Tahun: 2005

Versi: Revisi


Learning outcomes

Learning Outcomes

Pada akhir pertemuan ini, diharapkan mahasiswa

akan mampu :

  • Mahasiswa dapat menghitung penduga selang dari rataan, proporsi dan varians.


Outline materi

Outline Materi

  • Selang nilai tengah (rataan)

  • Selang beda nilai tengah (rataan)

  • Selang proporsi dan beda proporsi

  • Selang varians dan proporsi varians


Interval estimation

Interval Estimation

  • Interval Estimation of a Population Mean:

    Large-Sample Case

  • Interval Estimation of a Population Mean:

    Small-Sample Case

  • Determining the Sample Size

  • Interval Estimation of a Population Proportion

[--------------------- ---------------------]

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Interval estimation of a population mean large sample case

Interval Estimation of a Population Mean:Large-Sample Case

  • Sampling Error

  • Probability Statements about the Sampling Error

  • Constructing an Interval Estimate:

    Large-Sample Case with  Known

  • Calculating an Interval Estimate:

    Large-Sample Case with  Unknown


Sampling error

Sampling Error

  • The absolute value of the difference between an unbiased point estimate and the population parameter it estimates is called the sampling error.

  • For the case of a sample mean estimating a population mean, the sampling error is

    Sampling Error =


Interval estimate of a population mean large sample case n 30

Interval Estimate of a Population Mean:Large-Sample Case (n> 30)

  • With  Known

    where: is the sample mean

    1 - is the confidence coefficient

    z/2 is the z value providing an area of

    /2 in the upper tail of the standard

    normal probability distribution

    s is the population standard deviation

    n is the sample size


Interval estimate of a population mean large sample case n 301

Interval Estimate of a Population Mean:Large-Sample Case (n> 30)

  • With  Unknown

    In most applications the value of the population standard deviation is unknown. We simply use the value of the sample standard deviation, s, as the point estimate of the population standard deviation.


Interval estimation of a population mean small sample case n 30 with unknown

Interval Estimation of a Population Mean:Small-Sample Case (n < 30) with  Unknown

  • Interval Estimate

    where 1 - = the confidence coefficient

    t/2 = the t value providing an area of /2 in the upper tail of a t distribution

    with n - 1 degrees of freedom

    s = the sample standard deviation


Contoh soal apartment rents

Contoh Soal: Apartment Rents

  • Interval Estimation of a Population Mean:

    Small-Sample Case (n < 30) with  Unknown

    A reporter for a student newspaper is writing an

    article on the cost of off-campus housing. A sample of 10 one-bedroom units within a half-mile of campus resulted in a sample mean of $550 per month and a sample standard deviation of $60.

    Let us provide a 95% confidence interval estimate of the mean rent per month for the population of one-bedroom units within a half-mile ofcampus. We’ll assume this population to be normally distributed.


Contoh soal apartment rents1

Contoh Soal: Apartment Rents

  • t Value

    At 95% confidence, 1 -  = .95,  = .05, and /2 = .025.

    t.025 is based on n - 1 = 10 - 1 = 9 degrees of freedom.

    In the t distribution table we see that t.025 = 2.262.


Estimation of the difference between the means of two populations independent samples

Estimation of the Difference Between the Means of Two Populations: Independent Samples

  • Point Estimator of the Difference between the Means of Two Populations

  • Sampling Distribution

  • Interval Estimate of Large-Sample Case

  • Interval Estimate of Small-Sample Case


Sampling distribution of

Sampling Distribution of

  • Properties of the Sampling Distribution of

    • Expected Value

    • Standard Deviation

      where: 1 = standard deviation of population 1

      2 = standard deviation of population 2

      n1 = sample size from population 1

      n2 = sample size from population 2


Interval estimate of 1 2 large sample case n 1 30 and n 2 30

Interval Estimate of 1 - 2:Large-Sample Case (n1> 30 and n2> 30)

  • Interval Estimate with 1 and 2 Known

    where:

    1 -  is the confidence coefficient

  • Interval Estimate with 1 and 2 Unknown

    where:


Contoh soal par inc

Contoh Soal: Par, Inc.

  • 95% Confidence Interval Estimate of the Difference Between Two Population Means: Large-Sample Case, 1 and 2 Unknown

    Substituting the sample standard deviations for the population standard deviation:

    = 17 + 5.14 or 11.86 yards to 22.14 yards.

    We are 95% confident that the difference between the mean driving distances of Par, Inc. balls and Rap, Ltd. balls lies in the interval of 11.86 to 22.14 yards.


Interval estimate of 1 2 small sample case n 1 30 and or n 2 30

Interval Estimate of 1 - 2:Small-Sample Case (n1 < 30 and/or n2 < 30)

  • Interval Estimate with  2 Known

    where:


Contoh soal specific motors

Contoh Soal: Specific Motors

  • 95% Confidence Interval Estimate of the Difference Between Two Population Means: Small-Sample Case

    = 2.5 + 2.2 or .3 to 4.7 miles per gallon.

    We are 95% confident that the difference between the

    mean mpg ratings of the two car types is from .3 to 4.7 mpg (with the M car having the higher mpg).


Inferences about the difference between the proportions of two populations

Inferences About the Difference Between the Proportions of Two Populations

  • Sampling Distribution of

  • Interval Estimation of p1 - p2

  • Hypothesis Tests about p1 - p2


Sampling distribution of1

Sampling Distribution of

  • Expected Value

  • Standard Deviation

  • Distribution Form

    If the sample sizes are large (n1p1, n1(1 - p1), n2p2,

    and n2(1 - p2) are all greater than or equal to 5), the

    sampling distribution of can be approximated

    by a normal probability distribution.


Interval estimation of 2

Interval Estimation of 2

  • Interval Estimate of a Population Variance

    where the values are based on a chi-square distribution with n - 1 degrees of freedom and where 1 -  is the confidence coefficient.


Interval estimation of 21

Interval Estimation of 2

  • Chi-Square Distribution With Tail Areas of .025

.025

.025

95% of the

possible 2 values

2

0


Pertemuan 16 pendugaan parameter

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