Ketidakpastian Estimasi

# Pengaruh Ukuran Sampel terhadap Selang Kepercayaan

# Sampel 1
n1 <- 5
mean1 <- 50
sd1 <- 10
alpha <- 0.05

t1 <- qt(1-alpha/2, df = n1-1)
error1 <- t1*sd1/sqrt(n1)
interval1 <- c(mean1-error1, mean1+error1)
lebar1 <- interval1[2]-interval1[1]

interval1

## [1] 37.58336 62.41664

lebar1

## [1] 24.83328

# Sampel 2
n2 <- 30
mean2 <- 50
sd2 <- 10

t2 <- qt(1-alpha/2, df = n2-1)
error2 <- t2*sd2/sqrt(n2)
interval2 <- c(mean2-error2, mean2+error2)
lebar2 <- interval2[2]-interval2[1]

interval2

## [1] 46.26594 53.73406

lebar2

## [1] 7.468123

# Sampel 3
n3 <- 100
mean3 <- 50
sd3 <- 10

t3 <- qt(1-alpha/2, df = n3-1)
error3 <- t3*sd3/sqrt(n3)
interval3 <- c(mean3-error3, mean3+error3)
lebar3 <- interval3[2]-interval3[1]

interval3

## [1] 48.01578 51.98422

lebar3

## [1] 3.968434

# Tabel hasil
hasil_n <- data.frame(
  "Ukuran Sampel" = c(5,30,100),
  "Lebar Interval" = c(lebar1,lebar2,lebar3)
)

hasil_n

##   Ukuran.Sampel Lebar.Interval
## 1             5      24.833280
## 2            30       7.468123
## 3           100       3.968434

# Pengaruh Variabilitas Data terhadap Selang Kepercayaan

# Standar deviasi 10
nA <- 30
meanA <- 50
sdA <- 10

tA <- qt(1-alpha/2, df = nA-1)
errorA <- tA*sdA/sqrt(nA)
intervalA <- c(meanA-errorA, meanA+errorA)
lebarA <- intervalA[2]-intervalA[1]

intervalA

## [1] 46.26594 53.73406

lebarA

## [1] 7.468123

# Standar deviasi 50
nB <- 30
meanB <- 50
sdB <- 50

tB <- qt(1-alpha/2, df = nB-1)
errorB <- tB*sdB/sqrt(nB)
intervalB <- c(meanB-errorB, meanB+errorB)
lebarB <- intervalB[2]-intervalB[1]

intervalB

## [1] 31.32969 68.67031

lebarB

## [1] 37.34061

# Standar deviasi 90
nC <- 30
meanC <- 50
sdC <- 90

tC <- qt(1-alpha/2, df = nC-1)
errorC <- tC*sdC/sqrt(nC)
intervalC <- c(meanC-errorC, meanC+errorC)
lebarC <- intervalC[2]-intervalC[1]

intervalC

## [1] 16.39345 83.60655

lebarC

## [1] 67.2131

# Tabel hasil
hasil_sd <- data.frame(
  "Standar Deviasi" = c(10,50,90),
  "Lebar Interval" = c(lebarA,lebarB,lebarC)
)

hasil_sd

##   Standar.Deviasi Lebar.Interval
## 1              10       7.468123
## 2              50      37.340614
## 3              90      67.213105

# Pengaruh Pengetahuan Standar Deviasi Populasi

n <- 30
mean_x <- 50
sd_x <- 50
alpha <- 0.05

# Sigma diketahui (Distribusi z)
z <- qnorm(1-alpha/2)
error_z <- z*sd_x/sqrt(n)
interval_z <- c(mean_x-error_z, mean_x+error_z)
lebar_z <- interval_z[2]-interval_z[1]

interval_z

## [1] 32.10806 67.89194

lebar_z

## [1] 35.78388

# Sigma tidak diketahui (Distribusi t)
t <- qt(1-alpha/2, df = n-1)
error_t <- t*sd_x/sqrt(n)
interval_t <- c(mean_x-error_t, mean_x+error_t)
lebar_t <- interval_t[2]-interval_t[1]

interval_t

## [1] 31.32969 68.67031

lebar_t

## [1] 37.34061

# Tabel hasil
hasil_sigma <- data.frame(
  "Kondisi" = c("Sigma diketahui", "Sigma tidak diketahui"),
  "Lebar Interval" = c(lebar_z, lebar_t)
)

hasil_sigma

##                 Kondisi Lebar.Interval
## 1       Sigma diketahui       35.78388
## 2 Sigma tidak diketahui       37.34061