SORULAR/QUESTIONS 1. Bir operasyonun 80 adet on gözlemi yap?lmm? ve 28 gözlemde
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SORULAR/QUESTIONS 1. Bir operasyonun 80 adet on gözlemi yap?lmm? ve 28 gözlemde operatörün bos durdu?u gözlenmi?tir Daha sonra 40 adet gözlem daha yap?lmi?tir ve 17 gözlemde operatörün bos durdu?u gözlenmi?tir Hata oran %5 ve güvenlik düzeyi 99 % olacak ?ekilde i? örne?i almak istenmektedir. Kaç tane gözlem yap?lmas? gereklidir? (15 puan) // 80 observations are taken for an operation and in 28 of them the operator was idle. Then 40 observation more are taken and in 17 of them the operator was idle. If you want to take sample keeping the margin of error in 5% and confidence level at 99 %, how many observations are needed? (15 points) 2. Bir i? örneklemesi çal??mas?nda a?a?ida verilen form doldurulmu?tur. 1? yerinde günde 8 saat çal???l?yorsa üretken zaman? hesaplay?n?z? (10 puan) I/ In a work sampling study, the following form was filled. If the company is working 8 hours/day calculate the productive time? (10 points) Machine running/ Calisiyor Machine idle/ Bo 3. 08:30-18:00 saatleri aras?nda çal??an bir i?yerinde 10 adet gözlem yap?lmas? planlanmaktadir. Bu amaçla birincisi 0,15 ikincisi 0,9 olan ve tek say?h gözlemler 0,2 artacak, cift say?ls gözlemler 0.2 azalacak ?ekilde 10 adet rassal sayi üretilmi?tir. 6, ve 9. gözlem hangi satte yap?lmad?r? dsyerinde 10:30-10:45, 12:00-13:15, 15:30-15:50 saatleri aras?nda mola uygulanmaktad?r.) (20 puan) //Making 10 observations are planned in a workplace among employees between hours 8.30-18:00. For this purpose 10 numbers are generate randomly that first observation is 0,15 and odd numbers will increase 0.2, second observation is 0,9 and even numbers will decrease 0.2. In which hours should be done the observation number 6 and 9? (There are breaks in this workplace between hours 10:30-10-45, 12:00- 13:30, 15:30-15:50,) (20 points)Explanation / Answer
Proportion of idle for 80 operators = 28/80 = 0.34
Proportion of idle for 40 operators = 17/40 = 0.425
Taking average of proportions, p = 0.375
Now, Margin of error = z * [{p* (1-p)} / n] ^1/2
where , n = sample size, margin of error is = 5% , Z value for CI 99% is 2.58
hence, 0.05 = 2.58 * (0.2343 / n)^1/2
= 0.00037 = 0.2343 / n
= N = 0.2343/ 0.00037 = 633
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