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11111 Essay

1506 words - 7 pages

Exercise (18-33)
18.n=610 ;P̂x =50.7=.507
1­α =.99 α=.01, α/2=.005 , 1­α/2 =.995 100(1- α) % C.I for P̂x is given by:
P̂x-Z α/2√ P̂(1-P̂x)n <Px <P̂x + Z α/2√ P̂(1-P̂x)n
=.507-2.575√.507(1-.507)610<Px <.507+2.575√.507(1-.507)610
=.4548< Px < .5591
19(a). n=189 ;X=132; P̂x =xn=132189=.6984
1­α =.90 α=.10, α/2=.05 , 1­α/2 =.95 ...view middle of the document...

6119-1.96√.6119*.3881134 <Px<.6119+1.96√.6119*.3881134
=.5294 <Px<.6944
22.(a) n=95 ;X=29; P̂x =xn=2995=.3052
1­α =.99 α=.01, α/2=.005 , 1­α/2 =.995 100(1- α) % C.I for P̂x is given by:
P̂x-Z α/2√ P̂(1-P̂x)n <Px <P̂x + Z α/2√ P̂(1-P̂x)n
=.3052-2.575√.3052(1-.3052)95<Px <.3052+2.575√.3052(1-.3052)95
=.183< Px < .426
(b) Narrower
23. n=96 ;X=32; P̂x =xn=3296=.3333
1­α =.80 α=.20, α/2=.10 , 1­α/2 =.90 100(1- α) % C.I for P̂x is given by:
P̂x-Z α/2√ P̂(1-P̂x)n <Px <P̂x + Z α/2√ P̂(1-P̂x)n
=.3333-1.285√.3333(1-.3333)96<Px <.3333+1.285√.3333(1-.3333)96
=.2714< Px < .3951
24. n=198; X=98 P̂x =98198=.4949
100(1- α) % C.I for P̂x is given by:
P̂x-Z α/2√ P̂(1-P̂x)n <Px <P̂x + Z α/2√ P̂(1-P̂x)n
P̂x-Z α/2√ P̂(1-P̂x)n =.445
=>.4949--Z α/2 √ .4949(1-.4949)198 =.445
=> Z α/2 .4949*.506198 =.4949-.445
=> Z α/2 *0.0355 =0.0499
=> Z α/2 =1.40
=>P( Z <α/2) =.9192
=>1- P( Z >α/2) =.9192
=> P( Z >α/2) =1-.9192
=> P( Z >α/2 ) =.0808
=> α/2 =.0808*2
=> α =.1616
=>1- α =1-.1616
=>1- α =.8384
25.n=15; Sx=.880;V=n-1=15-1=14
1­α =.95 α=.05, α/2=.025 , 1­α/2 =.975
sx(n-1)Xv,α/2<σx< sx(n-1)Xv,1-α/2
=.880(15-1)X14,.025 <σx< .880(15-1)X14,.975
=.7744*1426.12 <σx<.7744*145.63
=.4150 <σx< 1.925
26.n=7;V=6
∑Xi=79+73+68+77+86+71+69=523
X̅=∑Xin=5237=74.714
∑Xi=79+73+68+77+86+71+69 =39321
Sx=∑Xi-nx̅n-1=39321-7*(74.714)6=40.954
1­α =.80 α=.20, α/2=.10 , 1­α/2 =.90
100(1- α) % C.I for σx is given by:
sx(n-1)Xv,α/2<σx< sx(n-1)Xv,1-α/2
=40.954(7-1)X6,.10 <σx< 40.954(7-1)X6,.90
=245.72410.64 <σx< 245.7242.20
=23.09 <σx< 111.692

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