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Tugas Mandiri (Individu) :

  Buatkan 1 contoh Kasus (dan jawaban penyelesaiannya)  untuk

permasalahan Estimasi !"#$TI!% ME$% (& 'ietahui n * +,)-

• 'ari soal tersebut dibuatan untu .on/dence #evel 0, dan 02-

• (contoh terlampir)• Tugas diupload di 3inusmaya

====================================================================================4uestion :$ survey was taken of "-5- companies that do business with /rms in India-One of the 6uestions on the survey was:Approximately how many years has your company been trading with rms in India?A random sample of 77 responses  to this uestion yielded a mean o8 1,-722years!

"uppose the population standard deviation for this uestion is 9-9 years!#sing this information$ construct a 0, con/dence interval for  the meannumber o8 years that a company has been trading in India 8or thepopulation o8 "-5- companies trading with /rms in India-

"ntu .on/dence #evel 0, :

$nswer:

Interpretation :

 %he analyst is &'( condent that if a

census of all #!"! companies trading

with rms in india were taken at the

time of this sur)ey$ the actual

population mean number of years a

company would ha)e been trading with

rms in India would be between *!+,+

and -.!/0+

"ntu .on/dence #evel 02 :

$nswer :

Interpretation :

 %he analyst is &'( condent that if a

census of all #!"! companies trading with

rms in india were taken at the time of 

this sur)ey$ the actual population mean

number of years a company would ha)e

been trading with rms in India would be

between *!+,+ and -.!/0+

365.12545.8

91.1455.1091.1455.10

44

7.7645.1455.10

44

7.7645.1455.10

645.1confidence%90

.44 ,7.7,455.10

2/2/

≤≤

+≤≤−

+≤≤−

+≤≤−

=⇒

===

 µ 

 µ 

 µ 

σ  µ 

σ 

σ 

α α 

n Z  X 

n Z  X 

 Z 

nand  X 

..............

.....455.10........455.10

44

............455.10

44

............455.10

......confidence%95

.44 ,7.7,455.10

2/2/

≤≤

+≤≤−

+≤≤−

+≤≤−

=⇒

===

 µ 

 µ 

 µ 

σ  µ 

σ 

σ 

α α 

n Z  X 

n Z  X 

 Z 

nand  X 

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 %amara 1adia2 -3'-/'30,'

4ontoh soal:

-! "uper)isor ingin mengestimasi waktu rata2rata yang dibutuhkan olehsebuah mesin baru untuk memproduksi - rim kertas! "ampel acakse5umlah /0 rim menun5ukan waktu rata2rata yang dibutuhkan adalah-$+ menit setiap rim nya! 6e)iasi standar dari waktu produksi adalah'$/' menit! 7aka buat estimasi inter)al dengan tingkat kepercayaan&'(8

 9awab:

a! %ingkat kepercayaan &'(

6iketahui:´ X   = -$+ menit

σ   = '$/' menit

n  = /0 rim

&'( condence = Z   = -$0,+

6i5awab:

´ X   2Z  α 

2  !σ 

√ n   ≤    μ   ≤   ´ X   Z  α 

2  !σ 

√ n

-$+ ; -$0,+ !0,30

√ 36   ≤    μ   ≤  -$+ -$0,+ !0,30

√ 36  

-$+ ; '$'*. ≤    μ   ≤  -$+ '$'*.

-$,-* ≤    μ   ≤  -$+*.

<esimpulan:

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 9adi estimasi waktu yang dibutuhkan untuk menghasilkan kertasdengan menggunakan tingkat kepercayaan &'( adalah antara -$,-*dan -$+*. dalam satuan menit!

b! %ingkat kepercayaan &+(

6iketahui:

´ X   = -$+ menit

σ   = '$/' menit

n  = /0 rim

&+( condence = Z   = -$&0

6i5awab:

´ X   2Z  α 

2  !σ 

√ n   ≤    μ   ≤   ´ X   Z  α 

2  !σ 

√ n

-$+ ; -$&0 !0,30

√ 36   ≤    μ   ≤  -$+ -$&0 !0,30

√ 36  

-$+ ; '$'&* ≤    μ   ≤  -$+ '$'&*

-$,'. ≤    μ   ≤  -$+&*

<esimpulan: 9adi estimasi waktu yang dibutuhkan untuk menghasilkan kertasdengan menggunakan tingkat kepercayaan &+( adalah antara -$,'.dan -$+&* dalam satuan menit!