Ejemplos Resueltos de Intervalos de Confianza para La Proporción

 

KVRABÍVRNFA NN

KIKMTLHV9 NERKZWALHV BK FHEGNAEYA TAZA LA TZHTHZFNÖE 1.  Ke uea N.K bk Keskñaeza Vkfuebarna `ay 044 alumehs matrnfulabhs. A uea mukstra sklkffnheaba alkathrnamketk alkathrnamketk bk ue 1;% bk kllhs, sk lks prkcuetö sn u utnlnzajae tnlnzajae kl fagktíe bk la nestntufnöe. Fhetkstarhe ekcatnvamketk ue thtal bk :2 alumehs. Falfular kl netkrvalh bk fhegnaeza bkl >;% para kstnmar la prhphrfnöe bk alumehs quk utnlnzae kl fagktíe. VHL[FNÖE

>7  = Ó4.0 ̊ =  =  1:4 1   = >;% >;%,, 1   = 4.>;, >;,  = 4.4 4.4;;  √  = √.  = . = 1.>7  (√) √ .(√.) √ .Ó.  KR =      Ó  √  =       Ó   √   =      Ó   =   467;ÓÓ 4.>:6 >:6 = 4.4663 4663  KR = 4.467; >7 Ó 4.4 4.466 6633 = 4.0  4.4771 4771 = 4.3 4.362 62  ̊  √ Ó  = 44.0.0 1.>7Ó A = ̊ >7 Ó 4.4.4663 4663 = 4.0 4.0++ 4.4771 4771 =4.077  ̊ + √ Ó  = 4.0 + 1.>7Ó J = ̊ _4.362 ≢  ≢ 4.077] = >;%  Kl vkrbabkrh valhr bk la prhphrfnöe bk alumehs quk utnlnzae kl fagktíe kstá fhmprkebnbh ketrk 4.362 y 4.077 neflunbh lhs kxtrkmhs fhe ue envkl bk fhegnaeza bkl >;% E= 044, e = 1;% 044 = 1:4, x9 utnlnzae kl fagktíe9 1:4-:2 = >7 alumehs  

:.  [e gajrnfaetk bk rkprhbufthrks bk BWB utnlnza ue fheiueth bk prukjas amplnas para kvaluar la guefnöe klîftrnfa bk su prhbufth. Rhbhs lhs rkprhbufthrks bk BWB bkjke pasar thbas las prukjas aetks bk vkebkrsk. [ea mukstra alkathrna bk ;44 rkprhbufthrks tnkek fhmh rksultabh 1; quk gallae ke uea h más prukjas. Kefuketrk ue netkrvalh bk fhegnaeza bk >4% para la prhphrfnöe bk lhs rkprhbufthrks bk BWB bk la phjlafnöe quk eh pasaríae thbas las prukjas. VHL[FNÖE    ,   e = ;44, x = 1;,    √ √. √. .

4.>4, 4, = 4.1144 ̊ =  = 4.46 1   = 4.>   =    =   =   = 1.72 √. )) =  ..( (.) ) =  ..  = 4.44376  KR =  (√   )=  ..((  Ó  = 44.4.466  1.72Ó 72 Ó 4.4437 443766 = 4.446 6  4.41:; 41:; = 4.4413; 13;   ̊  √ Ó A = ̊  = 44.4.466 + 1.72Ó 72 Ó 4.4437 443766 = 4.446+ 6 + 4.41:; 41:; = 4.442:; 2:;   ̊ + √ Ó Ó J = ̊ _4.413; ≢  ≢ 4.42:;] = >4%  Kl vkrbabkrh valhr bk la prhphrfnöe bk BWBV bk la phjlafnöe quk eh pasaríae thbas las prukjas kstá fhmprkebnbh ketrk 4.413; y 4.42:; neflunbh lhs kxtrkmhs fhe ue envkl bk fhegnaeza bkl >4%

6.  Ke ue kstubnh bk 644 affnbketks bk authmövnl ke uea fnubab kspkfígnfa, 74 tuvnkrhe fheskfukefnas gatalks. Fhe jask ke ksta mukstra, fhestruya ue netkrvalh bkl >;% bk fhegnaeza para aprhxnmar la prhphrfnöe bk thbhs lhs affnbketks authmhvnlístnfhs quk ke ksa fnubab tnkeke fheskfukefnas gatalks. VHL[FNÖE

 

KVRABÍVRNFA NN

e = 644, x = 74 fheskfukefnas gata gatalks lks

1   = >;% >;%,, 1   = 4.>;, >;,  = 4.4 4.4;;  √  = √.  = . = 1.>7  74  = 4.:  ̊ =  644 (√) .(√.) .(.) . KR =      =      =      =   = 4.4:61 A=  ̊ ̊  √ Ó  = 44.:.: 1.>7Ó >7 Ó 4.4 4.4:6 :611 = 4.:  4.42;6 42;6 = 4.1 4.1;; ;;  >7 Ó 4.4 4.4:6 :611 = 4.: + 4.42;6 42;6 = 4.: 4.:2; 2;   ̊ + √ Ó  = 44.:.:++ 1.>7Ó J = ̊ _4.1;; ≢  ≢ 4.:2;] = >;%  Kl vkrbabkrh valhr bk la prhphrfnöe bk thbhs lhs affnbketks authmhvnlístnfhs quk ke ksa fnubab tnkeke fheskfukefnas gatalks kstá fhmprkebnbh ketrk 4.1;; y 4.:2; neflunbh lhs kxtrkmhs fhe ue envkl bk fhegnaeza bkl >;%

(KIKZFNFNH BK TAZRNFNTAFNÖE TAZRNFNTAFNÖE KE LA VKVNÖE WNZR[AL)

2.  Kl nestntuth bk hpnenöe pùjlnfa utnlnzh uea mukstra alkathrna bk 744 klkfthrks quk afajae bk kmntnr su vhth, para rkalnzar uea prhykffnöe kstabístnfa kstabístnfa bk lhs rksultabhs. Vn kl shebkh nebnfa quk :24 klkfthrks vhtarhe a gavhr bkl faebnbath A, hjtkeca kl netkrvalh bk kstnmafnöebkl bkl>;%. phrfketaik bk klkfthrks a gavhr bk A ke thba la phjlafnöe fhe kl e envkl nvkl bk fhegnaeza VHL[FNÖE e = 744, x = :24

24 = 4.2  ̊ = :744 1   = 4.4.>; >; ↚  = 44.4.4;; ↚ √ = √.  = . = 1.>7  1 ̊)// =  .Ó. = 4.4:  KR = ∙ ̊ ( 1 A= J=

= 4.2 ‖ 1.>7 P 4.4: = 4.2  ‖ 4.46>:=4.6740

 Ó  Ó= 4.2 +1.>7 P 4.4: = 4.2 + 4.46>:= 4.26>:  ̊ ̊+√√ Ó Ó _4.671 ≢  ≢ 4.26>] = >;% 

Kl vkrbabkrh valhr bk la prhphrfnöe bk klkfthrks a gavhr bkl faebnbath A ksta fhmprkebnbh ketrk 4.671 y 4.26> neflunbh lhs kxtrkmhs fhe ue envkl bk fhegnaeza bkl >;%.