ufpi-intervalos de confiança
DESCRIPTION
slides com assunto da disciplina probabilidade e estatística lecionado pela professora da UFPITRANSCRIPT
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 1/19
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 2/19
µ σ
µ
σ
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 3/19
µ σ
µ
σ
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 4/19
µ σ
µ
σ
− α
α
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 5/19
µ σ
µ
σ
µ σ
Z = x − µσ√ n
− α
P (
−Z α
≤Z
≤Z α
) =
−α
P
−Z α
≤ x −µσ√ n
≤ Z α
=
− α
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 6/19
µ σ
µ
σ
P x − Z α
σ√ n ≤ µ ≤ x + Z α
σ√ n
= − α
µ
σ
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 7/19
µ σ
µ
σ
σ =
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 8/19
µ σ
µ
σ
µ σ
σ
σ
σ
x
x − µ
S
√ n
t = x − µ
S √ n
−
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 9/19
µ σ
µ
σ
− α
P (
−t α
≤t
≤t α
) =
−α
µ
σ
P (−t α
≤ x −µ
S √
n ≤t α
) =
−α
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 10/19
µ σ
µ
σ
P x − t α
S √ n ≤ µ ≤ x + t α
S √ n
=
− α
(n − )
µ σ
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 11/19
µ σ
µ
σ
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 12/19
µ σ
µ
σ
− α
σ
σ
S
(n− )S
σ
(n−
)
X n−
= (n −
)S
σ
P
(n− )S
X
sup ≤ σ ≤ (n− )S
X
inf
=
− α
ϕ = n −
σ
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 13/19
µ σ
µ
σ
n = S = − α = %
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 14/19
µ σ
µ
σ
P
S
(n −
)
X
sup
≤ σ ≤ S
(n −
)
X
inf
=
− α
ϕ = (n − )
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 15/19
µ σ
µ
σ
σf
pq n
Z = f − p
pq n
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 16/19
µ σ
µ
σ
− α
P (−Z α
≤ Z ≤ Z α
) = − α
P −Z α
≤ f −p √ pq n
≤ Z α
=
− α
P f − Z
α
pq n ≤ p ≤ f + Z
α
pq n= − α
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 17/19
µ σ
µ
σ
(n >
) q =
− p
(
−f )
P
f − Z α
f ( − f )
n ≤ p ≤ f + Z α
f ( − f )
n
= − α
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 18/19
µ σ
µ
σ
P
f − Z α
f ( −f )
n
N −nN −
≤ p ≤ f + Z α
f ( −f )
n
N −nN −
=
− α
7/17/2019 UFPI-Intervalos de Confiança
http://slidepdf.com/reader/full/ufpi-intervalos-de-confianca 19/19
µ σ
µ
σ