library(BSDA)
## Loading required package: lattice
## 
## Attaching package: 'BSDA'
## The following object is masked from 'package:datasets':
## 
##     Orange

Nomor 1

  1. Penghasilan perbulan karyawan pada sebuah perusahaan diketahui menyebar normal dengan simpangan baku Rp 600.000,-. Jika diambil sebanyak 16 contoh acak dari populasi tersebut, diperoleh rata-rata Rp 1.200.000,-. Tentukan selang kepercayaan 95% bagi nilai tengah populasi karyawan perusahaan tersebut
zsum.test(mean.x=1200000,sigma.x=600000, n.x=16, alternative="two.sided", conf.level = 0.95)
## 
##  One-sample z-Test
## 
## data:  Summarized x
## z = 8, p-value = 1.244e-15
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##   906005.4 1493994.6
## sample estimates:
## mean of x 
##   1200000

Nomor 2

tsum.test(mean.x=254, s.x = 3, n.x = 18, mean.y = 225, s.y = 2,
  n.y = 27, alternative = "greater", var.equal = TRUE,
  conf.level = 0.95)
## 
##  Standard Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 38.983, df = 43, p-value < 2.2e-16
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  27.74943       NA
## sample estimates:
## mean of x mean of y 
##       254       225

Nomor 3

before<-c(57,69,56,67,  55, 56, 62, 67, 67, 56)
after<-c(55,    70, 56, 65, 54, 55, 64, 65, 67, 54)
t.test(before,after,paired=TRUE, alternative="greater", mu=0.5)
## 
##  Paired t-test
## 
## data:  before and after
## t = 0.44598, df = 9, p-value = 0.3331
## alternative hypothesis: true difference in means is greater than 0.5
## 95 percent confidence interval:
##  -0.1220671        Inf
## sample estimates:
## mean of the differences 
##                     0.7

Nomor 4

tsum.test(mean.x=25, s.x = 6.4, n.x = 20, mean.y = NULL, mu=20, s.y = NULL,  n.y = NULL, alternative = "two.sided", var.equal = TRUE,
  conf.level = 0.95)
## 
##  One-sample t-Test
## 
## data:  Summarized x
## t = 3.4939, df = 19, p-value = 0.002429
## alternative hypothesis: true mean is not equal to 20
## 95 percent confidence interval:
##  22.00471 27.99529
## sample estimates:
## mean of x 
##        25

Nomor 5

IR64<-c(4.5, 5.0, 4.8, 4.0, 4.0, 3.9, 3.6, 4.8, 3.8)
MSP<-c(6.4, 5.9, 7.0, 6.5, 6.2, 8.0, 4.2, 3.8, 
4.0, 2.5, 5.8, 3.6)
tsum.test(mean.x=mean(IR64), s.x = sd(IR64), n.x = length(IR64), mean.y = mean(MSP), s.y = sd(MSP),  n.y = length(MSP), mu=2, alternative = "two.sided", var.equal = TRUE,
  conf.level = 0.95)
## 
##  Standard Two-Sample t-Test
## 
## data:  Summarized x and y
## t = -5.3258, df = 19, p-value = 3.86e-05
## alternative hypothesis: true difference in means is not equal to 2
## 95 percent confidence interval:
##  -2.2602512  0.1435846
## sample estimates:
## mean of x mean of y 
##  4.266667  5.325000

Nomor 6

X1<-c(4.8,  4,  5,  4.6,    5.4,    4.9,    4.3,    5.2,    5.1,    4.7,    5.4,    5.8)
X2<-c(5.5,4.1,5.2,4.5,5,5.3,4.8,4.5,6,4.7,5.3,5.4)
t.test(X1,X2,paired=TRUE, alternative="greater")
## 
##  Paired t-test
## 
## data:  X1 and X2
## t = -0.66753, df = 11, p-value = 0.7409
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -0.3382811        Inf
## sample estimates:
## mean of the differences 
##             -0.09166667

Nomor 7

tsum.test(mean.x=520000, s.x = 90000, n.x = 20, mean.y = NULL, mu=500000, s.y = NULL,  n.y = NULL, alternative = "greater", var.equal = TRUE,
  conf.level = 0.95)
## 
##  One-sample t-Test
## 
## data:  Summarized x
## t = 0.99381, df = 19, p-value = 0.1664
## alternative hypothesis: true mean is greater than 5e+05
## 95 percent confidence interval:
##  485201.9       NA
## sample estimates:
## mean of x 
##    520000

Nomor 8

#a.
tsum.test(mean.x=14.93, s.x = 1.781, n.x = 22, mu=16, mean.y = NULL, s.y = NULL,  n.y = NULL, alternative = "less", var.equal = TRUE,
  conf.level = 0.95)
## 
##  One-sample t-Test
## 
## data:  Summarized x
## t = -2.8179, df = 21, p-value = 0.005153
## alternative hypothesis: true mean is less than 16
## 95 percent confidence interval:
##        NA 15.58338
## sample estimates:
## mean of x 
##     14.93
#b
tsum.test(mean.x=21.66, s.x = 2.386, n.x = 12, mean.y = 20.68, s.y = 1.985,  n.y = 10, alternative = "two.sided", var.equal = TRUE,
  conf.level = 0.95)
## 
##  Standard Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.0335, df = 20, p-value = 0.3137
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.9979425  2.9579425
## sample estimates:
## mean of x mean of y 
##     21.66     20.68
#c

Nomor 9

tsum.test(mean.x=40, s.x = 6, n.x = 10, mean.y = 50, s.y = 10.2,  n.y = 10, alternative = "two.sided", var.equal = TRUE,
  conf.level = 0.90)
## 
##  Standard Two-Sample t-Test
## 
## data:  Summarized x and y
## t = -2.6722, df = 18, p-value = 0.01554
## alternative hypothesis: true difference in means is not equal to 0
## 90 percent confidence interval:
##  -16.489199  -3.510801
## sample estimates:
## mean of x mean of y 
##        40        50

Nomor 10

prop.test(28, 90, p = 0.25, alternative = "two.sided",
          correct = TRUE)
## 
##  1-sample proportions test with continuity correction
## 
## data:  28 out of 90, null probability 0.25
## X-squared = 1.4815, df = 1, p-value = 0.2235
## alternative hypothesis: true p is not equal to 0.25
## 95 percent confidence interval:
##  0.2199763 0.4185873
## sample estimates:
##         p 
## 0.3111111

Nomor 11

tsum.test(mean.x=37900, s.x = 5100, n.x = 12, mean.y = 39800, s.y = 5900,  n.y = 12, alternative = "two.sided", var.equal = FALSE,
  conf.level = 0.95)
## 
##  Welch Modified Two-Sample t-Test
## 
## data:  Summarized x and y
## t = -0.84396, df = 21.549, p-value = 0.408
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -6574.576  2774.576
## sample estimates:
## mean of x mean of y 
##     37900     39800

Nomor 12

before<-c(57,69,56,67,  55, 56, 62, 67, 67, 56)
after<-c(55,    70, 56, 65, 54, 55, 64, 65, 67, 54)
t.test(before,after,paired=TRUE, alternative="greater", mu=0.5)
## 
##  Paired t-test
## 
## data:  before and after
## t = 0.44598, df = 9, p-value = 0.3331
## alternative hypothesis: true difference in means is greater than 0.5
## 95 percent confidence interval:
##  -0.1220671        Inf
## sample estimates:
## mean of the differences 
##                     0.7

Nomor 13

xbar= 163.5
mu0 = 162
sig = 6
n = 100
z = (xbar-mu0)/(sig/sqrt(n))
z
## [1] 2.5
alpha = .05
z.alpha = qnorm(1-alpha)
z.alpha
## [1] 1.644854
pnorm(z, lower.tail=FALSE)
## [1] 0.006209665

Nomor 14

prop.test(15, 40, p = 0.4, alternative = "two.sided",
          correct = FALSE)
## 
##  1-sample proportions test without continuity correction
## 
## data:  15 out of 40, null probability 0.4
## X-squared = 0.10417, df = 1, p-value = 0.7469
## alternative hypothesis: true p is not equal to 0.4
## 95 percent confidence interval:
##  0.2422298 0.5296756
## sample estimates:
##     p 
## 0.375

Nomor 15

prop.test(x = c(275, 100), n = c(500, 250), alternative="greater", correct=FALSE)
## 
##  2-sample test for equality of proportions without continuity
##  correction
## 
## data:  c(275, 100) out of c(500, 250)
## X-squared = 15, df = 1, p-value = 5.376e-05
## alternative hypothesis: greater
## 95 percent confidence interval:
##  0.08725794 1.00000000
## sample estimates:
## prop 1 prop 2 
##   0.55   0.40

Nomor 16

before<-c(100,250,150,200,300,275,170,210)
after<-c(250,300,135,250,350,250,150,200)
t.test(before,after,paired=TRUE, alternative="greater")
## 
##  Paired t-test
## 
## data:  before and after
## t = -1.3679, df = 7, p-value = 0.8932
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -68.56957       Inf
## sample estimates:
## mean of the differences 
##                  -28.75

Nomor 17

#a
before<-c(68,79,58,65,89,72,69,56,58,54,65,61,50,57)
after<-c(60,76,52,60,78,73,67,52,54,55,61,56,52,50)
t.test(before,after,paired=TRUE, alternative="greater", mu=2, correct=FALSE)
## 
##  Paired t-test
## 
## data:  before and after
## t = 1.9901, df = 13, p-value = 0.03402
## alternative hypothesis: true difference in means is greater than 2
## 95 percent confidence interval:
##  2.212348      Inf
## sample estimates:
## mean of the differences 
##                3.928571
#b
tsum.test(mean.x=4.86, s.x = 3.98, n.x = 7, mean.y = 3, s.y = 3.27,  n.y = 7, alternative = "two.sided", var.equal = TRUE,
  conf.level = 0.95)
## 
##  Standard Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 0.95536, df = 12, p-value = 0.3582
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.38196  6.10196
## sample estimates:
## mean of x mean of y 
##      4.86      3.00

Nomor 18

sedang<-c(45,50,38,48,38,40,48)
tinggi<-c(60,55,47,46,35,38,50)
t.test(sedang,tinggi,paired=TRUE, alternative="two.sided", var.equal=FALSE)
## 
##  Paired t-test
## 
## data:  sedang and tinggi
## t = -1.353, df = 6, p-value = 0.2248
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -9.629342  2.772199
## sample estimates:
## mean of the differences 
##               -3.428571

Nomor 19

tsum.test(mean.x=1, s.x = 0.5, n.x = 10, mean.y = 1.7, s.y = 0.8,  n.y = 10, alternative = "two.sided", var.equal = TRUE,
  conf.level = 0.95)
## 
##  Standard Two-Sample t-Test
## 
## data:  Summarized x and y
## t = -2.3464, df = 18, p-value = 0.0306
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -1.32676529 -0.07323471
## sample estimates:
## mean of x mean of y 
##       1.0       1.7

Nomor 20

xbar= 203
mu0 = 200
sig = 16
n = 25
z = (xbar-mu0)/(sig/sqrt(n))
z
## [1] 0.9375
alpha = .05
z.alpha = qnorm(1-alpha)
z.alpha
## [1] 1.644854
pnorm(z, lower.tail=FALSE)
## [1] 0.1742507

Nomor 21

prop.test(11, 200, p = 0.1, alternative = "two.sided",
          correct = FALSE)
## 
##  1-sample proportions test without continuity correction
## 
## data:  11 out of 200, null probability 0.1
## X-squared = 4.5, df = 1, p-value = 0.03389
## alternative hypothesis: true p is not equal to 0.1
## 95 percent confidence interval:
##  0.03098534 0.09578700
## sample estimates:
##     p 
## 0.055

Nomor 22

PakanA<-c(4.6,5.0,4.7,4.1,4.0,3.8,3.6,4.8,3.8,4.2)
PakanB<-c(6.5,5.9,7.0,6.4,6.3,8.0,4.6,3.9,4.2,4.5,5.8,3.9)
t.test(PakanA,PakanB,paired=FALSE, alternative="less", var.equal=TRUE)
## 
##  Two Sample t-test
## 
## data:  PakanA and PakanB
## t = -2.9575, df = 20, p-value = 0.003892
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##        -Inf -0.5516185
## sample estimates:
## mean of x mean of y 
##  4.260000  5.583333

Nomor 23

zsum.test(mean.x=350000,sigma.x=1500, n.x=12, alternative="two.sided", conf.level = 0.90)
## 
##  One-sample z-Test
## 
## data:  Summarized x
## z = 808.29, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 90 percent confidence interval:
##  349287.8 350712.2
## sample estimates:
## mean of x 
##    350000

Nomor 24

tsum.test(mean.x=32, s.x = 8.6, n.x = 25, mean.y = NULL, mu=30, s.y = NULL,  n.y = NULL, alternative = "two.sided", var.equal = TRUE,
  conf.level = 0.90)
## 
##  One-sample t-Test
## 
## data:  Summarized x
## t = 1.1628, df = 24, p-value = 0.2563
## alternative hypothesis: true mean is not equal to 30
## 90 percent confidence interval:
##  29.05728 34.94272
## sample estimates:
## mean of x 
##        32

Nomor 25

solusi1<-c(112, 75, 119, 94, 91, 94, 93, 76, 88, 96)
solusi2<-c(82, 86, 100, 97, 88, 89, 86, 83, 89, 97, 86, 85, 81, 101)
tsum.test(mean.x=mean(solusi1), s.x = sd(solusi1), n.x = length(solusi1), mean.y = mean(solusi2), s.y = sd(solusi2),  n.y = length(solusi2), alternative = "two.sided", var.equal = TRUE, conf.level = 0.95)
## 
##  Standard Two-Sample t-Test
## 
## data:  Summarized x and y
## t = 1.0737, df = 22, p-value = 0.2946
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -4.204936 13.233507
## sample estimates:
## mean of x mean of y 
##  93.80000  89.28571

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