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CI for Two Population PropKelompok 8

Muhammad Fa

Muhammad

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EQUATION

Confidence interval 100%(1 - ) for difference two population prop2are :

or

1

12/2121

2

22

1

112/21

1()(

)1()1()(

n

pZppPP

n

pp

n

ppZpp

2

22

1

112/21

)1()1()(

n

pp

n

ppZpp

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EXPLANATION

= 1st total population from data sample

= 2nd total population from data sample

= sample data in population 1

= sample data in population 2

= 1st population porportion from data sample

= 2nd population porportion from data sample

1p

1n

2n

2p

n

xp

1x

1x

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TEMPLATE

1. Collect all information from the data and determine the value table II

2. The end points of the confidence interval for p1p2are:

3. Interprete the confidence interval

2

22

1

112/21

)1()1()(

n

pp

n

ppZpp

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EXAMPLE

A study of teenage suicide included a sample of 125 boys abetween ages of 12 and 16 years selected scientifically fromrecords to a private psychiatric hospital. Suicide attempts were reof the boys and 60of the girls. We assume that the girls consti

random sample from a population of similar girls and likewboys. Construct a 95%confidence interval for the difference betwproportions !

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Collect all information from the da

Let is the population of boys and is the population of girlssucidie

From 95% confidence interval we get:

So we get Z/2from table II:

100

125

2

1

n

n

25.0100/25

48.0125/60

2

1

p

p

0.050.95-1

96.1Z /2

0.025/2

1p 2p

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The end points of the confidence interval fo

2

22

1

112/21 )

1(

)

1(

)(n

ppn

ppZpp

125)48.01(48.096.1)25.048.0( =

100

75.0(25.0

125

)52.0(48.096.1)23.0(

0019.00.00296.1)23.0(

=

=0039.096.1)23.0( = = .1)23.0(

= 0.12223.0

352.0108.0

0.12223.0 0.12223.0

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Interprete the confidence interva

We interprete this interval that the differences between the twproportion, p1p2= 0.23. We are 95% confident that the differenboys and girls who try to suicide is somewhere between 0.108 0

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CASES

CEWEK

3 2 2 3

6 4 3 1

3 3 2 2

3 5 2 3

3

COWOK

1 1 7

2 2 10

1 4 2

3 1

Data diatas adalah studi mengenai waktu para mahasiswa menonton tv selama 2jmahasiswi dan 14 mahasiswa. Dari studi tersebut diketahui ada sebanyak 5 mahasiswyang menonton selama 2 jam. Buatlah selang kepercayaan 90% dari selisih 2 proporsi d

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PENYELESAIAN

17

14

2

1

n

n

29.017/5

36.014/5

2

1

p

p 0.10.90-1

65.1Z /20.05/2

2

22

1

112/21

)1()1()(

n

pp

n

ppZpp

14

36.01(36.065.1)29.036.0(

17

0(29.0

14

)64.0(36.0

65.1)07.0(

0121.00165.065.1)07.0(

0286.065.1)07.0(

)2805.0()07.0( 2105.0 35.0