Goodness of Fit

Lab 6 - Unit 5


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Exercise 1

Please work out in R by doing a chi-squared test on the treatment (X) and improvement (Y) columns in treatment.csv.

Data Exercise 1

e1 <- read.csv("treatment.csv")
e1

Jawaban dan Penjelasan Exercise 1

H0 : kedua variabel independent
H1 : kedua variabel dependent

cont.e1 = table(e1$treatment, e1$improvement);cont.e1
##              
##               improved not-improved
##   not-treated       26           29
##   treated           35           15
chisq.test(cont.e1,simulate.p.value = TRUE)
## 
##  Pearson's Chi-squared test with simulated p-value (based on 2000
##  replicates)
## 
## data:  cont.e1
## X-squared = 5.5569, df = NA, p-value = 0.03098

Berdasarkan hasil di atas, nilai p-value (0.02999) lebih kecil dari tingkat signifikan (0.05). Dengan demikian, H0 ditolak yang artinya kedua variabelnya (treatment dan improvement) dependent.

Exercise 2

Find out if the cyl and carb variables in mtcars dataset are dependent or not.

Data Exercise 2

DT::datatable(mtcars)

Jawaban dan Penjelasan Exercise 2

H0 : kedua variabel independent
H1 : kedua variabel dependent

cyl = mtcars$cyl
carb = mtcars$carb

chisq.test(cyl, carb)
## 
##  Pearson's Chi-squared test
## 
## data:  cyl and carb
## X-squared = 24.389, df = 10, p-value = 0.006632

Berdasarkan hasil di atas, nilai p-value (0.006632) lebih kecil dari tingkat signifikan (0.05). Dengan demikian, H0 ditolak yang artinya kedua variabelnya (cly dan carb) dependent.

Exercise 3

256 visual artists were surveyed to find out their zodiac sign. The results were: Aries (29), Taurus (24), Gemini (22), Cancer (19), Leo (21), Virgo (18), Libra (19), Scorpio (20), Sagittarius (23), Capricorn (18), Aquarius (20), Pisces (23). Test the hypothesis that zodiac signs are evenly distributed across visual artists.

Data Exercise 3

n = 256
zodiac = c(29,24,22,19,21,18,19,20,23,18,20,23) 
pert.zodiac = zodiac/n 
expected = c(rep(256/12, 12))

e3 = data.frame(
  "zodiak" = c('Aries', 'Taurus' , 'Gemini' , 'Cancer' , 'Leo' , 'Virgo' , 'Libra' , 'Scorpio', 'Sagittarius', 'Capricorn', 'Aquarius', 'Pisces'),
  "observed" = zodiac,
  'expected' = expected
)
e3

Jawaban dan Penjelasan Exercise 3

H0 : semua zodiak terdistribusi dengan baik
H1 : terdapat zodiak yang tidak terdistribusi dengan baik

chisq = sum((zodiac-expected)^2 / expected)
pchisq(q = chisq, df = 12-1, lower.tail=F)
## [1] 0.9265414

Berdasarkan hasil di atas, nilai pchisq (0.9265414) lebih besar dari tingkat signifikan (0.05). Dengan demikian, H0 diterima yang artinya semua zodiak terdistribusi dengan baik.