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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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