Uji Hipotesis Dua Sampel Pertemuan – 3 Uji Hipotesis Dua Sampel [ Bagian 1 ]

Comparing two populations – Some Examples Is there a difference in the mean value of residential real estate sold by male agents and female agents in south Florida? Is there a difference in the mean number of defects produced on the day and the afternoon shifts at Kimble Products? Is there a difference in the mean number of days absent between young workers (under 21 years of age) and older workers (more than 60 years of age) in the fast-food industry? Is there is a difference in the proportion of Ohio State University graduates and University of Cincinnati graduates who pass the state Certified Public Accountant Examination on their first attempt? Is there an increase in the production rate if music is piped into the production area? ALFIRA SOFIA

Comparing Two Population Means No assumptions about the shape of the populations are required. The samples are from independent populations. The formula for computing the value of z is: ALFIRA SOFIA

EXAMPLE 1 The U-Scan facility was recently installed at the Byrne Road Food-Town location. The store manager would like to know if the mean checkout time using the standard checkout method is longer than using the U-Scan. She gathered the following sample information. The time is measured from when the customer enters the line until their bags are in the cart. Hence the time includes both waiting in line and checking out. ALFIRA SOFIA

EXAMPLE 1 continued Step 1: State the null and alternate hypotheses. H0: µS ≤ µU H1: µS > µU Step 2: State the level of significance. The .01 significance level is stated in the problem. Step 3: Find the appropriate test statistic. Because both samples are more than 30, we can use z-distribution as the test statistic. ALFIRA SOFIA

Example 1 continued Step 4: State the decision rule. Reject H0 if Z > Z Z > 2.33 ALFIRA SOFIA

Example 1 continued Step 5: Compute the value of z and make a decision The computed value of 3.13 is larger than the critical value of 2.33. Our decision is to reject the null hypothesis. The difference of .20 minutes between the mean checkout time using the standard method is too large to have occurred by chance. We conclude the U-Scan method is faster. ALFIRA SOFIA

Two-Sample Tests about Proportions Beberapa contoh : Wakil presiden sumber daya manusia ingin mengetahui apakah terdapat perbedaan proporsi pekerja, yang dibayar per jam, yang tidak masuk lebih dari 5 hari kerja per tahun di pabrik Atlanta dan Houston. General Motors tengah mempertimbangkan sebuah rancangan baru untuk Pontiac G6. Rancangan tsb. ditunjukkan kepada sekelompok calon pembeli berusia di bawah 30 tahun dan kelompok lainnya yang berusia di atas 60 tahun. Pontiac ingin mengetahui apakah ada perbedaan dalam proporsi kedua kelompok yang menyukai rancangan baru tersebut. Seorang konsultan bagi industri penerbangan sedang menyelidiki ketakutan terbang di antara orang-orang dewasa. Secara spesifik, perusahaan tersebut ingin mengetahui apakah terdapat perbedaan dalam proporsi laki-laki dibanding perempuan yang takut terbang. ALFIRA SOFIA

Two Sample Tests of Proportions Kita ingin menguji apakah proporsi dua sampel berasal dari populasi yang setara. The two samples are pooled (dikumpulkan) using the following formula. ALFIRA SOFIA

Two Sample Tests of Proportions continued The value of the test statistic is computed from the following formula. ALFIRA SOFIA

Two Sample Tests of Proportions - Example Manelli Perfume Company baru-baru ini mengembangkan sebuah parfum baru yang rencananya akan dipasarkan dengan merek Heavenly. Sejumlah penelitian pasar mengindikasikan bahwa Heavenly memiliki potensi pasar yang sangat baik. Departemen Penjualan di Manelli ingin mengetahui apakah terdapat perbedaan dalam proporsi perempuan yang lebih muda dan lebih tua yang akan membeli Heavenly jika wewangian tersebut dipasarkan. Ada dua populasi yang saling bebas, satu populasi terdiri atas perempuan yang lebih muda dan satu populasi terdiri atas perempuan yang lebih tua. Masing-masing perempuan yang ditarik sampelnya akan diminta untuk mencoba wewangian Heavenly dan memberikan indikasi apakah ia cukup menyukai wewangian itu untuk membeli satu botol. ALFIRA SOFIA

Two Sample Tests of Proportions - Example Step 1: State the null and alternate hypotheses. H0: 1 =  2 H1:  1 ≠  2 Step 2: State the level of significance. The .05 significance level is stated in the problem. Step 3: Find the appropriate test statistic. We will use the z-distribution ALFIRA SOFIA

Two Sample Tests of Proportions - Example Step 4: State the decision rule. Reject H0 if Z > Z/2 or Z < - Z/2 Z > 1.96 or Z < -1.96 ALFIRA SOFIA

Two Sample Tests of Proportions - Example Step 5: Compute the value of z and make a decision Nilai z hitung sebesar 2,21 berada di daerah penolakan. Sehingga, hipotesis nol ditolak pada tingkat signifikansi 0,05. Dengan kata lain, kita menolak hipotesis bahwa proporsi perempuan muda yang akan membeli parfum Heavenly sama dengan proporsi perempuan tua yang akan membeli parfum tersebut. ALFIRA SOFIA

Referensi Aczel, Amir D., and Jayavel Sounderpandian (2006), Complete Business Statistics, 6th edition, McGraw Hill. Levine, David M. (2008), Statistics for Managers : using Microsoft Excel, 5th Edition, Pearson Education. Lind, Douglas A. (2008), Statistical Techniques in Business & Economics, 13th Edition, McGraw Hill. Lind, Douglas A. (2007), Teknik-teknik Statistika dalam Bisnis dan Ekonomi Menggunakan Data Global, jilid 1, Edisi 13, Erlangga. Lind, Douglas A. (2008), Teknik-teknik Statistika dalam Bisnis dan Ekonomi Menggunakan Data Global, jilid 2, Edisi 13, Erlangga.

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