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#               AULA 17 - IC para proporcao                  #
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rm(list = ls()); cat('\014')

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# Exemplo 1

# amostra
n = 200
pbarra = 160/n
pbarra

s = sqrt(pbarra * (1 - pbarra))
s

# confianca e significancia
gama = 0.95
alfa = 1 - gama

# estatistica (variancia conhecida)
z = qnorm(1 - alfa/2)
z

# intervalo otimista
L = pbarra - z*s/sqrt(n)
U = pbarra + z*s/sqrt(n)

c(L, U)


# intervalo conservativo
p = 0.5
sigma = sqrt(p*(1-p))
sigma

L = pbarra - z*sigma/sqrt(n)
U = pbarra + z*sigma/sqrt(n)


##############################################################
# Exemplo 2: tamanho amostra propocao usando proporcao previa

# erro maximo
E = 0.05 

# confianca e significancia
gama = 0.99
alfa = 1 - gama
z = qnorm(1 - alfa/2)
z

# tamanho da amostra
p = 0.20
sigma2 = p*(1-p)
sigma2

n = (z^2*sigma2)/(E^2)
n


##############################################################
# Exemplo 3: tamanho de amostra caso conservador

# erro maximo
E = 0.02 

# confianca e significancia
gama = 0.95
alfa = 1 - gama
z = qnorm(1 - alfa/2)
z

# tamanho da amostra
p = 0.5
sigma2 = p*(1-p)
sigma2

n = (z^2*sigma2)/(E^2)
n