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#               AULA 19 - Testes de Hipoteses                #
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rm(list = ls()); cat('\014')

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# Exemplo:  Teste para a média de uma população com variância conhecida

# erro tipo 1 = alfa
alfa = 0.05

# hipoteses de duas caudas
# valor de ztab para o erro  tipo 1
qnorm(alfa/2)
qnorm(1-alfa/2)


# Encontrando ponte de corte
n = 20
xcorte1 = 350 + sqrt(3^2/n)*(-1.96)
xcorte1

xcorte2 = 350 + sqrt(3^2/n)*(1.96)
xcorte2


# Encontrando o valor p
n = 20
mu = 350
sigma = 3
xbarraobs = 346

ztab = (xbarraobs - mu)/sqrt(sigma^2/n)
ztab

2*pnorm(-5.96)


###########################################################################
# Exemplo: Teste para a média de uma população com variância desconhecida

# erro tipo 1 = alfa
alfa = 0.05

n = 20
mu = 350
s = 5
xbarraobs = 346

ttab = (xbarraobs - mu)/sqrt(s^2/n)
ttab

2*pt(-3.6, n-1)