Statistics Homework

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??=(
2.575 à5.8 2
)
2
= 56
?? ??95% Ê??
???
0.0015
0.310 1.9925 Ê?75
= (0.30965, 0.31035)
??=(
21.96 à0.0015 2
)
0.0005
= 35
?? ??99% Ê??
???
15
230 3.2498 Ê?10
= (214.58,245.42)
??(??) = ??(?
??(??) = ??(?
????
1
??
) = ? ??(???? ) = ?? = ??
??
??
??
????
1
??
??2
) = 2 ? ??(???? ) = 2 ?? 2 =
??
??
??
??
1
??(?? 2 ) = ??{ ?(???? ? ??)2
??
1
= ?? [ ?{(???? ? ??) + (?? ? ??)}2 ]
??
1
= ?? [ ?{(???? ? ??)2 + 2(???? ? ??)(?? ? ???? ) + (?? ? ??)2 } ]
??
= ??(??) ? 2??{(?? ? ??)2 } + ??{(?? ? ??)2 } = ??(??) ? ??(???????? )
1
??{ ?(???? ? ??)(?? ? ??)} = ???{(?? ? ??)2 } = ?????????
??
(?? ? 1)
??2
??(?? 2 ) = ??(??) ? ???????? (??) = ?? 2 ?
= ??2
??
??
2
?(??
??
?
??)
??
?? 2 = ??2
=
???1
???1
a.
??(??) = ????
??????(??) = ??(?? 2 ) = ????(1 ? ??)
??(??) ????
??(??) =
=
=??
??
??
b.
??(??? ) =
???
(??(??) + 2 )
?? + ???
=
???
(???? + 2 )
(?? + ???)
???
5.62 6.32
???? = (78.3 ? 87.2) 1.985 à(?
+
)
50
50
= ?8.9 2.3662
= (?11.2662, ?6.5338)
???? = (84 ? 77)
2.7633
à(?(
11 à42 + 17 à62
1
1
)è + ))
28
12 18
= 7 5.4631
= (1.5369,12.4631)
???? = (36300 ? 38100)
2.8188
à(?(
11 à50002 + 11 à61002
1
1
)è + ))
22
12 12
= ?1800 6417.9595
= (?8217.9595,4617.9595)
a.
??=
114
= 0.57
200
0.57 à0.43
= 0.57 2.0537 à?
200
= (0.4981,0.6419)
b.
0.57 à0.43
???????????????? ?????????? = 2.0537 à?
200
= 0.0350
???????? ?????? ?????????? = 500 ? 15
= 485
485
??=
= 0.97
500
90% ???? = 0.97 1.645 à?
0.97 à0.03
500
= (0.9575,0.9825)

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