Pertemuan 16 Pendugaan Parameter
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Pertemuan 16Pendugaan ParameterMatakuliah: I0134 Metoda StatistikaTahun: 2005Versi: Revisi
Learning OutcomesPada akhir pertemuan ini, diharapkan mahasiswa akan mampu :Mahasiswa dapat menghitung penduga selang dari rataan, proporsi dan varians.
Outline MateriSelang nilai tengah (rataan)Selang beda nilai tengah (rataan)Selang proporsi dan beda proporsiSelang varians dan proporsi varians
Interval EstimationInterval Estimation of a Population Mean: Large-Sample CaseInterval Estimation of a Population Mean: Small-Sample CaseDetermining the Sample SizeInterval Estimation of a Population Proportion[--------------------- ---------------------][--------------------- ---------------------][--------------------- ---------------------]
Interval Estimation of a Population Mean:Large-Sample CaseSampling ErrorProbability Statements about the Sampling ErrorConstructing an Interval Estimate: Large-Sample Case with KnownCalculating an Interval Estimate: Large-Sample Case with Unknown
Sampling ErrorThe 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 isSampling Error =
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 > 30)With UnknownIn 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 UnknownInterval 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 RentsInterval 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 of campus. Well assume this population to be normally distributed.
Contoh Soal: Apartment Rentst ValueAt 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.
Area in Upper Tail
Estimation of the Difference Between the Means of Two Populations: Independent SamplesPoint Estimator of the Difference between the Means of Two PopulationsSampling DistributionInterval Estimate of Large-Sample CaseInterval Estimate of Small-Sample Case
Sampling Distribution of Properties of the Sampling Distribution of Expected Value
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 (n1 > 30 and n2 > 30)Interval Estimate with 1 and 2 Known
where:1 - is the confidence coefficientInterval Estimate with 1 and 2 Unknown
Contoh Soal: Par, Inc.95% Confidence Interval Estimate of the Difference Between Two Population Means: Large-Sample Case, 1 and 2 UnknownSubstituting 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 (n1 < 30 and/or n2 < 30)Interval Estimate with 2 Known
Contoh Soal: Specific Motors95% 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 themean 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 PopulationsSampling Distribution of Interval Estimation of p1 - p2Hypothesis Tests about p1 - p2
Sampling Distribution of Expected Value
Distribution FormIf the sample sizes are large (n1p1, n1(1 - p1), n2p2,and n2(1 - p2) are all greater than or equal to 5), thesampling distribution of can be approximatedby a normal probability distribution.
Interval Estimation of 2Interval 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 2Chi-Square Distribution With Tail Areas of .025 95% of thepossible 2 values20.025.025
Selamat Belajar Semoga Sukses.