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Pendugaan Parameter Nilai Tengah Pertemuan 13 Matakuliah: L0104 / Statistika Psikologi Tahun : 2008

Bina Nusantara Learning Outcomes 3 Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menghitung pendugaan parameter nilai tengah satu atau dua populasi.

Bina Nusantara Outline Materi 4 Penduigaan nilai tengah satu populasi Pendugaan beda dua nilai tengah sampel besar Pendugaan beda nilai tengah sampel kecil Pendugaan beda nilai tengah populasi tidak bebas

Bina Nusantara [--------------------- ---------------------]  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

Bina Nusantara Interval Estimate of a Population Mean: Large-Sample Case (n > 30) With σ  Known where: is the sample mean 1 -α is the confidence coefficient zα/2 is the z value providing an area of α/2 in the upper tail of the standard normal probability distribution s is the population standard deviation n is the sample size

Bina Nusantara Interval Estimate of a Population Mean: Large-Sample Case (n > 30) With σ  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.

Bina Nusantara Interval Estimation of a Population Mean: Small-Sample Case (n < 30) Population is Not Normally Distributed The only option is to increase the sample size to n > 30 and use the large-sample interval-estimation procedures. Population is Normally Distributed and σ is Known The large-sample interval-estimation procedure can be used. Population is Normally Distributed and σ is Unknown The appropriate interval estimate is based on a probability distribution known as the t distribution.

Bina Nusantara Interval Estimation of a Population Mean: Small-Sample Case (n < 30) with σ Unknown Interval Estimate where 1 -α = the confidence coefficient tα/2 = the t value providing an area of α/2 in the upper tail of a t distribution with n - 1 degrees of freedom s = the sample standard deviation

Bina Nusantara Interval Estimate with σ 1 and σ 2 Known where: 1 - α is the confidence coefficient Interval Estimate with σ 1 and σ 2 Unknown where: Interval Estimate of  1 -  2: Large-Sample Case (n1 > 30 and n2 > 30)

Bina Nusantara Point Estimator of the Difference Between the Means of Two Populations Population 1 Par, Inc. Golf Balls  1 = mean driving distance of Par distance of Par golf balls Population 1 Par, Inc. Golf Balls  1 = mean driving distance of Par distance of Par golf balls Population 2 Rap, Ltd. Golf Balls  2 = mean driving distance of Rap distance of Rap golf balls Population 2 Rap, Ltd. Golf Balls  2 = mean driving distance of Rap distance of Rap golf balls m 1 –  2 = difference between the mean distances the mean distances Simple random sample Simple random sample of n 1 Par golf balls of n 1 Par golf balls x 1 = sample mean distance for sample of Par golf ball Simple random sample Simple random sample of n 1 Par golf balls of n 1 Par golf balls x 1 = sample mean distance for sample of Par golf ball Simple random sample Simple random sample of n 2 Rap golf balls of n 2 Rap golf balls x 2 = sample mean distance for sample of Rap golf ball Simple random sample Simple random sample of n 2 Rap golf balls of n 2 Rap golf balls x 2 = sample mean distance for sample of Rap golf ball x 1 - x 2 = Point Estimate of m 1 –  2

Bina Nusantara Interval Estimate of μ 1 - μ 2 : Small-Sample Case (n1 < 30 and/or n2 < 30) Interval Estimate with σ 2 Known where:

Bina Nusantara Interval Estimate of μ 1 - μ 2 : Small-Sample Case (n1 < 30 and/or n2 < 30) Interval Estimate with σ 2 Unknown where:

Bina Nusantara Point Estimate of the Difference Between Two Population Means μ 1 = mean miles-per-gallon for the population of M cars μ 2 = mean miles-per-gallon for the population of J cars Point estimate of μ 1 - μ 2 = = 29.8 - 27.3 = 2.5 mpg. Contoh Soal: Specific Motors

Bina Nusantara 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). Contoh Soal: Specific Motors

Bina Nusantara Inference About the Difference Between the Means of Two Populations: Matched Samples With a matched-sample design each sampled item provides a pair of data values. The matched-sample design can be referred to as blocking. This design often leads to a smaller sampling error than the independent-sample design because variation between sampled items is eliminated as a source of sampling error.

Bina Nusantara Delivery Time (Hours) District OfficeUPX INTEX Difference Seattle 32 25 7 Los Angeles 30 24 6 Boston 19 15 4 Cleveland 16 15 1 New York 15 13 2 Houston 18 15 3 Atlanta 14 15 -1 St. Louis 10 8 2 Milwaukee 7 9 -2 Denver 16 11 5 Contoh Soal: Express Deliveries

Bina Nusantara Inference About the Difference Between the Means of Two Populations: Matched Samples Let μd = the mean of the difference values for the two delivery services for the population of district offices –Hypotheses H0: μd = 0, Ha: μd ≠ 0 –Rejection Rule – Assuming the population of difference values is approximately normally distributed, the t distribution with n - 1 degrees of freedom applies. With α =.05, t.025 = 2.262 (9 degrees of freedom). – Reject H0 if t 2.262 Contoh Soal: Express Deliveries

Bina Nusantara Inference About the Difference Between the Means of Two Populations: Matched Samples Conclusion Reject H 0. – There is a significant difference between the mean delivery times for the two services. Contoh Soal: Express Deliveries

Bina Nusantara Selamat Belajar Semoga Sukses

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