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Statistik Industri [12] December 6, 2008

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Mengerjakan latihan soal, dari buku Walpole no.10-32, 10-90, 11-14, 13-4.

Statistik Industri [11] November 28, 2008

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Soal untuk ujian akhir semester ini (kisi-kisi dari Bu Arian):
1. Uji hipotesa 1 sampel
2. Uji hipotesa 2 sampel (mean, variance)
3. Chi-square test
4. ANOVA
5. Simple linear regression and correlation

Masuk ke Bab 11 buku Walpole, pelajaran kali ini mengenai Regression Analysis.

Regresi bisa negatif (berbanding terbalik) atau positif (berbanding lurus). Ada single regression, ada multiple regression (dipengaruhi oleh lebih dari satu faktor).

Statistik Industri [10] November 22, 2008

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Mengulang sedikit pelajaran mengenai chi-square test, Bu Arian mengingatkan bahwa langkah pertama dalam uji hipotesa adalah: Menentukan hipotesa awal dan hipotesa alternatifnya.

Tujuh contoh soal, dalam bagian akhir soft copy bahan kuliah minggu sebelumnya, dijadikan tugas untuk dikumpulkan tanggal 28 November 2008.

ANOVA (analysis of variance)

Penjelasannya ada juga di http://en.wikipedia.org/wiki/Analysis_of_variance.

One-factor ANOVA computation

Penjelasannya ada juga di http://en.wikipedia.org/wiki/One-way_ANOVA.

Tambah 2 soal lagi (mengenai ANOVA di atas) untuk dikumpulkan pada minggu berikutnya…total jadi 9 soal dong!

😩

Statistik Industri [9] November 14, 2008

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CHI-SQUARE TEST

Materinya dari Bab 10.15 buku Walpole, Test for Independence (Categorical Data). Contoh: Melempar dadu sebanyak 120 kali, maka harapan (frekuensi ekspektasi, sesuai dengan teori distribusi seragam/normal) untuk keluarnya angka satu adalah 120/6 = 20 kali. Namun jika percobaan benar-benar dilakukan, hasilnya kemungkinan besar berbeda dari yang diharapkan.

Menguji dengan chi-square test dimulai dengan menentukan batas kritis untuk masing-masing kategori.

Menurut wikipedia, rumusnya:

rumus-chi-square

Contoh: 300 orang, 120 orang perempuan (12 kidal) dan 180 orang laki-laki

Ho: p1 = p2, proporsi perempuan kidal sama dengan proporsi laki-laki kidal

H1: p1 ≠ p2, proporsi orang kidal (baik perempuan maupun laki-laki) tidak sama, berarti tidak ada hubungannya dengan gender.

Jika sebelumnya uji dua proporsi menggunakan z-test, maka dengan menggunakan average proportion:

p =   12 + 24    =  36  = 0.12

      120 + 180       300

Jika proporsinya sama, maka untuk perempuan kidal:

Observed = 12, expected = 120 x 0.12 = 14.4

Setelah kategori lain juga dihitung lalu dimasukkan ke rumus di atas, didapat X2 = 0.6848 sementara nilai kritis X2U > 3.841, berarti X2 < X2U. Kesimpulannya, data tidak cukup untuk membuktikan bahwa proporsinya berbeda.

Kuliah terpaksa diakhiri pada saat baru 50 menit berjalan karena mati lampu… 😩

Statistik Industri [8] November 9, 2008

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Uji hipotesis.

Statistik Industri [7] October 26, 2008

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*I don’t know what to write…*

Hanya selintas-selintas saja memperhatikan pengajaran Bu Arian Dhini siang itu. Alasannya: Sibuk belajar untuk kuis Operations Research pada jam kuliah sesudahnya.

Dari softcopy yang kami peroleh di penghujung kelas, materinya adalah:

Bad news, dalam UTS Statistik Industri yang akan datang ternyata tidak jadi open book. Akhirnya akan open sheet (maksimal 2 lembar A4), hanya boleh menggunakan kalkulator dan tabel. Waks! Means no laptop?

😩

Statistik Industri [6] October 18, 2008

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ESTIMATION PROBLEMS

A point estimate is a single number. For the population mean (and population standard
deviation), a point estimate is the sample mean (and sample standard deviation).

A confidence interval provides additional information about variability.

PR:

1. What is meant by “the sampling distribution of the mean”?
2. What does the central limit theorem say? Why is it useful?
3. How is the population mean of the sample average related to the population mean of individual observations?
4. What is the standard error of the mean, and what do we use it for?
5. What happens to the sampling distribution of the mean if (i) the sample size is increased, (ii) the population standard deviation is decreased?
6. Using  4 your Standard Normal table, verify that :
– 90 % of the area under the standard normal curve (i.e N(0,1) corresponds to Z= ± 1.65;
– 95 % of the area under the standard normal curve corresponds to Z = ± 1.96
– 99 % of the area under the standard normal curve corresponds to Z = ± 2.58
7. Students in MA238 spend on average 3.75 hours a week studying ( with a population standard deviation σ = 5.17 )
i. Given this fact, describe the sampling distribution of the mean if all possible random sample size 50 were chosen.
ii. What can you say about the mean off all the possible sample means?
iii. If 250 such samples were chosen at random and for each you calculated a 95% C.I for the mean, how many such intervals would you expect to contain the true mean?
iv. If instead you calculated a 99% C.I. for the mean, how many intervals would you now expect to capture the true mean.
v. Would you expect the 99% C.I. for the mean to be narrower or wider than the corresponding 95 % C.I. for the mean. Justify your answer!
8. The director of quality at a light bulbs factory needs to estimate the average life of a large shipment of light bulbs. A random sample of 64 light bulbs indicated a sample average life 350 hours with sample standard deviation of 100 hours.
a) Construct and interpret a 95% confidence interval estimate of the true average life of light bulbs in this shipment.
b) Do you think the manufacturer has the right to state that the light bulbs last an average 400 hours? Explain.
c) Does the population have to be normally distributed here for the interval to be valid? Explain.
d) Explain why an observed of 320 hours is not unusual, even thought it outside it is outside the 95% confidence interval you have calculated.
e) Suppose that the sample average had been 300 hours. What would be your answer to a) ?
9. A newspaper headline describing a poll of registered voters taken two weeks before a recent election reads “Aitchison lead with 525. The accompanying article describing the poll state that the margin of the error was 2% with 95% confidence.
a) Explain in plain language to someone who knows no statistics what “95% confidence “ means?
b) The poll shows Aitchison leading. But the newspaper article said that the election was too close to call, Explain why?
10. A student  reads that a 95% confidence interval for the mean maths score leaving sert students in 45 to 47 %. Asked to explain the meaning of this interval, the student says, 95% of leaving cert students have math score between 451 and 47%. Is the student right? Justify your answer.

Statistik Industri [5] October 12, 2008

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Sesuai janjinya, Ibu Arian Dhini memberikan quiz. Soalnya diambil dari topik distribusi Poisson dan distribusi normal.

Statistik [4] September 28, 2008

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Quiz euy!!! Jangan lupa, belajar buat tanggal 11 Oktober 2008, bahannya sampai dengan Bab 6 buku Walpole.

SAMPLING DISTRIBUTION

Contoh:

A population is the set (possibly infinite) of all possible observations. A sample is a subset of a population.

Statistik Industri [3] September 21, 2008

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Continuous Probability Distribution

Distribusi normal: Mean (ÎŒ) menentukan titik tengah bell shaped curve, standar deviasi (σ) menunjukkan sebarannya.

Distribusi standar normal: ÎŒ = 0, σ = 1.

Pendekatan normal ke binomial bisa dipakai pada n mendekati tak hingga.

Distribusi eksponensial: ÎŒ = 1 / λ , σ = 1 / λ. Memoryless, kemunculan hasil sampling pada suatu interval waktu tidak mempengaruhi hasil yang lain.

Disebut distribusi gamma jika α = 1, banyak dipakai di teori antrian.

Waduh…kalau menurut buku Walpole, pelajarannya sudah sampai Bab 6 nih, kapan belajarnya ya?

PR untuk dikumpulkan tanggal 27 September 2008:
– Carilah sebuah jurnal internasional yang menggunakan distribusi probabilitas diskrit atau distribusi normal pada data dan pengolahannya.
– Jelaskan bagaimana datanya (level of measurementnya) dan cara pengumpulan datanya.
– Tuliskan kembali formula probabilitas yang digunakan dan jelaskan tujuan dari pemakaian distribusi pada penelitian tersebut.
– Berikan pendapat mengenai distribusi probabilitas yang digunakan!