Eneias

p = 0.2
n = 2400

x = rbinom(n, 1, p)
x

##    [1] 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0
##   [38] 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
##   [75] 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
##  [112] 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
##  [149] 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0
##  [186] 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0
##  [223] 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0
##  [260] 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
##  [297] 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
##  [334] 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0
##  [371] 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0
##  [408] 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
##  [445] 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0
##  [482] 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1
##  [519] 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0
##  [556] 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0
##  [593] 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0
##  [630] 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0
##  [667] 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [704] 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
##  [741] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0
##  [778] 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0
##  [815] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 0
##  [852] 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0
##  [889] 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0
##  [926] 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0
##  [963] 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1000] 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0
## [1037] 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0
## [1074] 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0
## [1111] 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## [1148] 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0
## [1185] 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0
## [1222] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## [1259] 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1
## [1296] 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0
## [1333] 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1
## [1370] 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0
## [1407] 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0
## [1444] 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0
## [1481] 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0
## [1518] 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
## [1555] 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0
## [1592] 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0
## [1629] 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0
## [1666] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
## [1703] 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## [1740] 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## [1777] 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [1814] 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1
## [1851] 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1
## [1888] 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1925] 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
## [1962] 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0
## [1999] 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1
## [2036] 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## [2073] 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0
## [2110] 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0
## [2147] 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0
## [2184] 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0
## [2221] 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
## [2258] 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1
## [2295] 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0
## [2332] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1
## [2369] 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0

mean(x)

## [1] 0.2195833

erro_padrao = sd(x)/sqrt(2400)
erro_padrao

## [1] 0.008451773

margem_erro = qnorm(0.975)*erro_padrao
margem_erro

## [1] 0.01656517

LI = mean(x) - margem_erro
LS = mean(x) + margem_erro
c(LI,LS)

## [1] 0.2030182 0.2361485

O intervalo com 95% de confiaça é de 0,18 e 0,21 dos eleitores do Eneias em Botafogo!

#————————————————-

Daciolo

p = 0.3
n = 1800

x = rbinom(n, 1, p)
x

##    [1] 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1
##   [38] 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0
##   [75] 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0
##  [112] 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0
##  [149] 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1
##  [186] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0
##  [223] 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0
##  [260] 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0
##  [297] 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0
##  [334] 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0
##  [371] 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0
##  [408] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0
##  [445] 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0
##  [482] 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1
##  [519] 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0
##  [556] 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0
##  [593] 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
##  [630] 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0
##  [667] 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1
##  [704] 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1
##  [741] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
##  [778] 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1
##  [815] 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
##  [852] 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0
##  [889] 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0
##  [926] 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0
##  [963] 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0
## [1000] 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0
## [1037] 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0
## [1074] 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0
## [1111] 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0
## [1148] 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1
## [1185] 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0
## [1222] 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0
## [1259] 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1
## [1296] 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1333] 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1
## [1370] 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1
## [1407] 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1
## [1444] 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1
## [1481] 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0
## [1518] 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1
## [1555] 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0
## [1592] 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0
## [1629] 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1
## [1666] 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0
## [1703] 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1
## [1740] 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0
## [1777] 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0

length (x)

## [1] 1800

mean(x)

## [1] 0.3033333

erro_padrao1 = sd(x) / sqrt(1800)
erro_padrao1

## [1] 0.0108382

margem_erro1 = qnorm(0.975)*erro_padrao1


LI1 = mean(x) - margem_erro1
LS1 = mean(x) + margem_erro1
c (LI1,LS1)

## [1] 0.2820909 0.3245758

#——————————

Intervalo com 90% de confiança dos eleitores do Tiririca na Tijuca

p = 0.15
n - 3600

## [1] -1800

x = rbinom (3600,1,0.15)
x

##    [1] 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0
##   [38] 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
##   [75] 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0
##  [112] 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0
##  [149] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0
##  [186] 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0
##  [223] 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0
##  [260] 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
##  [297] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0
##  [334] 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1
##  [371] 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0
##  [408] 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0
##  [445] 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
##  [482] 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0
##  [519] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
##  [556] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
##  [593] 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
##  [630] 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
##  [667] 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1
##  [704] 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
##  [741] 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
##  [778] 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0
##  [815] 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
##  [852] 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1
##  [889] 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0
##  [926] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
##  [963] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0
## [1000] 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0
## [1037] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1074] 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1111] 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0
## [1148] 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
## [1185] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## [1222] 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
## [1259] 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1
## [1296] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
## [1333] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## [1370] 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0
## [1407] 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
## [1444] 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0
## [1481] 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## [1518] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0
## [1555] 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0
## [1592] 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0
## [1629] 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
## [1666] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0
## [1703] 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0
## [1740] 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1
## [1777] 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0
## [1814] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
## [1851] 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0
## [1888] 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0
## [1925] 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0
## [1962] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0
## [1999] 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0
## [2036] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## [2073] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0
## [2110] 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0
## [2147] 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0
## [2184] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0
## [2221] 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## [2258] 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0
## [2295] 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## [2332] 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
## [2369] 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
## [2406] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0
## [2443] 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## [2480] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## [2517] 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [2554] 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
## [2591] 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
## [2628] 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0
## [2665] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
## [2702] 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## [2739] 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
## [2776] 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## [2813] 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0
## [2850] 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0
## [2887] 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1
## [2924] 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0
## [2961] 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
## [2998] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
## [3035] 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## [3072] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0
## [3109] 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0
## [3146] 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0
## [3183] 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0
## [3220] 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
## [3257] 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
## [3294] 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0
## [3331] 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0
## [3368] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
## [3405] 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0
## [3442] 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1
## [3479] 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
## [3516] 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0
## [3553] 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0
## [3590] 0 0 0 0 0 0 0 0 1 0 0

mean (x)

## [1] 0.1594444

erro_padrao2 = sd(x)/sqrt (3600)
erro_padrao2

## [1] 0.006102348

margem_erro2 = qnorm(0.95)*erro_padrao2
margem_erro2

## [1] 0.01003747

LI2 = mean(x) - margem_erro2
LS2 = mean(x) + margem_erro2
c(LI2,LS2)

## [1] 0.1494070 0.1694819

H0: p = 0.5 (a moeda é honesta) H1: p != 0.5 (moeda é viciada)
Teste de proporção
alpha: 0.05 (95% de confiança)

numero_de_caras <- 470:610
plot(numero_de_caras, dbinom(numero_de_caras, size=1000, prob=.541),type='h')

prop.test(541, 1000, p = 0.5, conf.level = 0.95)

## 
##  1-sample proportions test with continuity correction
## 
## data:  541 out of 1000, null probability 0.5
## X-squared = 6.561, df = 1, p-value = 0.01042
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.5095159 0.5721653
## sample estimates:
##     p 
## 0.541

REJ H0

Essa moeda é viciada!

#————————

7 caras em 10 lançamentos

Essa moeda é honesta?

alpha 0.05

numero_de_caras1 = 4:10

plot(numero_de_caras1, dbinom(numero_de_caras1, size=10, prob=.7),type="h")

prop.test(7, 10, p = 0.5, conf.level = 0.95)

## 
##  1-sample proportions test with continuity correction
## 
## data:  7 out of 10, null probability 0.5
## X-squared = 0.9, df = 1, p-value = 0.3428
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
##  0.3536707 0.9190522
## sample estimates:
##   p 
## 0.7

0.3536707 0.9190522

Aula 9 - Gráficos da Normal

Manuela Martins

27/01/2022

Eneias

O intervalo com 95% de confiaça é de 0,18 e 0,21 dos eleitores do Eneias em Botafogo!

Daciolo

Intervalo com 90% de confiança dos eleitores do Tiririca na Tijuca

REJ H0

Essa moeda é viciada!

7 caras em 10 lançamentos

Essa moeda é honesta?