hws51 - µ σ / n. X X µ X σx µ µ σx # σx $ σ/ n σ/...

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Unformatted text preview: µ σ / n. X X µ X σx µ µ σx # σx $ σ/ n σ/ n 25 !" $ 100 !$ σ/ n 6 !% & $ X ' ! ' ( + . σ µ 1 + , 2 72 x−u 72 ! 3% " X 3 + 55 − 50 1 .4 !# 3 , σ/ n , ) -. , 25 ( * , ( ! µ - - # - !% ! 4 X 5 # 6! # + " - ! ! !0 σ/ n ( ( -. - 3( ! # ( ( !/ * X X $ # !/ , -. X * 0 ) X x−u 55 − 50 σ/ n 7/ 4 !% 4X 5#6 # 4 5 !# 6 3 !#8 9 !# ≈ !#2!# 3 % 4 X 5#6 # ! 475 !% 6 !#8 9 !% !#2 !% " $ 4 ( : . µ nµ / 2 %# + ;47 5 2 !% 6 µ p = p = .3; σ p = ˆ ˆ µ p = p = .1; σ p = ˆ ˆ µ p = p = .6; σ p = ˆ ˆ > % 180 − 200 14 σ/ n 2 !% pq .3(.7) = = .0458 n 100 pq .1(.9) = = .015 n 400 pq .6(.4) = = .0310 n 250 , - 47 5 , -. pq .5(.5) = = .03162 n 250 p− p .66 − .5 475 6 475 6 σp .03162 + != % #% !# ! p ( ' - .83 − .8 6 47 5 !# !#2 !% $ ! " & 6 " .02 .76 − .8 .84 − .8 4 ?7 ? 6 42$? 7 ? $ $!% 3 6 3$ .02 .02 $ # @ $ !/ 4 p 5 !" 6 " % ! !#< !% " != " $ $ ˆ p 4!3 ? p ? !& 6 " % σp = ˆ - pq .8(.2) = = .02 n 400 µ p = p = .8; σ p = ˆ ˆ ' 4 3 xi & x−µ !& 4 p 5 !& 6 . nσ xi xi 5 & 6 σ 3( ! $ 72 4 # i =1 $ # - !# 47 5 # " ≈ ! 6 p 165 !" " 250 - :- !# A ! - > - p , σp = ˆ ˆ p − p) < −0.01 6 ˆ 4 p − p ) > 0.01 =% = $ ! $ # : :- -. - pq .25(.75) = = .02739 n 250 ˆ 8 ; 4 − 0.01 < ( p − p ) < 0.01 6 ˆ 8 ; 4 − 0.01 + p < p < 0.01 + p 6 ˆ (−0.01 + p ) − p p − p (0.01 + p ) − p < < 0.027 σp 0.027 ˆ 42 ! 3? 7 ? ! 3 6 2 $! % % !3 % 8; 2 µ ' &! ' # #8 σ " . " σ - ) # σ $ !" ! ( 3 * ( X & # µ σ / n ≈ $ !" 3 4X 5 =6 4X ? 36 & ' 100 $ " ! 3 1090 − 1085 47 5 6 2.167 1078 − 1085 47 ? 6 2.167 x 3 & ! 47 5 $ 6 ! !#2 !% = ! &" 47 5 2 !$ 6 ≈ - :- % , - ...
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This note was uploaded on 10/02/2009 for the course PSTAT 5E taught by Professor Eduardomontoya during the Spring '08 term at UCSB.

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