Written by 1. Seftika Anggraini
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2. Nur Anisa Dika Maharani
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3. Yudita Rasma Aminati
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4. Muhammad Aly Sa'id
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7. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents favor the construction while only 59 of 125 suburban residents are in favor. Is there a significant difference between the proportion of urban and suburban residents who favor construction of the nuclear plant? Use level of significance 0,04
√
⁄ ⁄ is rejected if ⁄or
⁄
-2.054
0
2.054
̂ ̂ ̂ ̂ √ ( ) √ ( )
because
so is rejected. So, there is no a significant difference between
the proportion of urban and suburban residents who favor construction of the nuclear plant
Test and CI for Two Proportions Sample 1 2
X 63 59
N 100 125
Sample p 0,630000 0,472000
Difference = p (1) - p (2) Estimate for difference: 0,158 96% CI for difference: (0,0229400; 0,293060) Test for difference = 0 (vs ≠ 0):
Z = 2,36
P -Value = 0,018
Fisher’s exact test: P -Value = 0,022
8. A cigarette industry produced two type brands of cigarette. it is found that 56 of 200 smokers like brand A and 29 of 150 smokes like brand B. Can we conclude in level of significance 0,06, when brand A sold exceed than brand B?
hypothesis level of significance Test statistic
√
critical region
is rejected if
0
X
1.555
calculation
̂ ̂ ̂ ̂ √ ( ) √ ( )
Decision because so is rejected. So, smokers like brand A than brand B and brand A sold exceed than brand B.
Test and CI for Two Proportions Sample 1 2
X 56 29
N 200 150
Sample p 0,280000 0,193333
Difference = p (1) - p (2) Estimate for difference: 0,0866667 94% lower bound for difference: 0,0163107 Test for difference = 0 (vs > 0): Z = 1,87
P-Value = 0,031
Fisher’s exact test: P -Value = 0,040
9. Seorang ahli genetika tertarik pada proporsi laki – laki dan perempuan, dalam suatu populasi yang menderita suatu kelainan darah. Dalam suatu contoh 100 laki – laki ternyata ada 31 yang menderita, sedangkan di antara 100 perempuan hanya 24 yang menderita kelainan tersebut. Dapatkah kita menyimpulkan pada taraf nyata 0,01 bahwa proporsi laki – laki yang menderita kelainan pada populasi tersebut lebih besar daripada perempuan yang menderita ?
hypothesis level of significance Test statistic
√
critical region
is rejected if
0
2.326
X
calculation
̂ ̂ ̂ ̂ √ ( ) √ ( )
Decision because so is accepted. Jadi, proporsi laki – laki yang menderita kelainan darah pada populasi tersebut kurang dari atau sama dengan perempuan yang menderita kelainan darah.
Test and CI for Two Proportions Sample 1 2
X 31 24
N 100 100
Sample p 0,310000 0,240000
Difference = p (1) - p (2) Estimate for difference: 0,07 99% lower bound for difference: -0,0764491 Test for difference = 0 (vs > 0): Z = 1,11 Fisher’s exact test: P -Value = 0,171
P-Value = 0,134
10. Sebuah penelitian ingin mengetahui apakah ikli m dingin membuat anak lebih sering membolos dari sekolah dibandingkan iklim yang lebih hangat. Dua kelompok seswa diambil secara acak, satu dari Maine dan satu lagi dari Alabama. Diantara 300 siswa dari Maine dan satu lagi dari Alabama. Di antara 300 siswa dari Maine, 72 anak membolos sekurang – kurangnya sehari selama semester berjalan.
hypothesis level of significance Test statistic
√
critical region
1.645 is rejected if
0
1.645
X
calculation
̂ ̂ ̂ ̂ √ ( ) √ ( )
Decision because so is accepted. Jadi, iklim dingin membuat anak lebih sering membolos dari sekolah dibandingkan iklim yang lebih hangat.
Test and CI for Two Proportions Sample 1 2
X 72 70
N 300 400
Sample p 0,240000 0,175000
Difference = p (1) - p (2) Estimate for difference: 0,065 95% lower bound for difference:
0,0137994
