CS-Lab6-Goodness-of-Fit

##7 EXERCISE

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

dataEX1 <- read.csv("treatment.csv")
table(dataEX1$treatment, dataEX1$improvement)

##              
##               improved not-improved
##   not-treated       26           29
##   treated           35           15

chisq.test(dataEX1$treatment, dataEX1$improvement, correct=FALSE)

## 
##  Pearson's Chi-squared test
## 
## data:  dataEX1$treatment and dataEX1$improvement
## X-squared = 5.5569, df = 1, p-value = 0.01841

Then, from the data treatment (X), and improvement (Y) from file treatment.csv, we got the chi-squared value of 5.5569 with the degree of freedom is 1 and the p value is 0.01841.

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

data(mtcars)
table(mtcars$cyl, mtcars$carb)

##    
##     1 2 3 4 6 8
##   4 5 6 0 0 0 0
##   6 2 0 0 4 1 0
##   8 0 4 3 6 0 1

df <- 1
alpha <- 0.05
chisq.test(mtcars$cyl, mtcars$carb)

## Warning in chisq.test(mtcars$cyl, mtcars$carb): Chi-squared approximation may be
## incorrect

## 
##  Pearson's Chi-squared test
## 
## data:  mtcars$cyl and mtcars$carb
## X-squared = 24.389, df = 10, p-value = 0.006632

The chi-squared value of 24.389 with the degree of freedom is 10 and the p value is 0.006632. Because the value of p value is very low than the significan level, then of course we reject the h0.

#7.3 256 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. (Reference)

We need to make the data into a data set, then we find the value of chisquared and p value.

zodiac <-c(29,24,22,19,21,18,19,20,23,18,20,23)
chisq.test(zodiac)

## 
##  Chi-squared test for given probabilities
## 
## data:  zodiac
## X-squared = 5.0938, df = 11, p-value = 0.9265

Now, we know that the chisquared value is 5.0938 and the p-value is 0.9265 that bigger than significance level, then because the pvalue is bigger than the significan level, we accept h0 that the zodiac signs are evenly distributed across visual artists.