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#           AULA 16 - Intervalos de Confianca                #
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rm(list = ls()); cat('\014')

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# Exemplo 1: IC para mu quando a variancia e conhecida


# populacao
mu = 350
sigma = 3

# amostra
n = 20
xbarra = 346

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

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

# intervalo
L = xbarra - z*sigma/sqrt(n)

U = xbarra + z*sigma/sqrt(n)

c(L, U)


##############################################################
# Exemplo 2: tamanho de amostra  

# populacao
sigma = 25

# amostra
E = 8 # erro maximo

# confianca e significancia
alfa = 0.01
z = qnorm(1 - alfa/2)
z

# tamanho da amostra
n = (z^2 * sigma^2)/(E^2)
n


##############################################################
# Exemplo 3: IC variancia desconhecida

# amostra
x = c(6, 6, 7, 8, 9, 9, 9, 10, 11, 12)

n = length(x)
n

xbarra = mean(x)
xbarra

s = sd(x)
s

# confianca e significancia
gama = 0.90
alfa = 1 - gama

# estatistica (variancia desconhecida)
t = qt(1 - alfa/2, n - 1)
t

# intervalo
L = xbarra - t*s/sqrt(n)

U = xbarra + t*s/sqrt(n)

c(L, U)