Anly 545 - Categorical Distribution

Data Set-up

set.seed(12345)
dice_group<-c(1:6)
dice_rolls<-6
dice_trials<-20000
dice_results<-matrix(nrow = dice_trials, ncol = dice_rolls)

for(i in 1:dice_trials){
  dice_results[i,]<-sample(dice_group,dice_rolls,replace=TRUE)
}

Create new success column

dice_success<-as.data.frame(dice_results)

dice_success$count<-
  ifelse((dice_success$V1==5|dice_success$V1==6),1,0)+
  ifelse((dice_success$V2==5|dice_success$V2==6),1,0)+
  ifelse((dice_success$V3==5|dice_success$V3==6),1,0)+
  ifelse((dice_success$V4==5|dice_success$V4==6),1,0)+
  ifelse((dice_success$V4==5|dice_success$V5==6),1,0)+
  ifelse((dice_success$V6==5|dice_success$V6==6),1,0)

Histogram *Data is not normal

hist(dice_success$count)

Test for Normality *Anderson- Darling test for large sample size

\(H_0\)= Data is normal \(H_1\)= Data is not normal

library(nortest)
ad.test(dice_success$count)

## 
##  Anderson-Darling normality test
## 
## data:  dice_success$count
## A = 584.24, p-value < 2.2e-16

• p-value is < 0.05. Thus we reject null hypothesis. Therefore, the data is not normal.

Binomial Test *Two tailed Binomial Test

colSums(dice_success!=0)

##    V1    V2    V3    V4    V5    V6 count 
## 20000 20000 20000 20000 20000 20000 17752

success<-17752
trials<-20000
probability<-1/6

binom.test(success, trials, probability)

## 
##  Exact binomial test
## 
## data:  success and trials
## number of successes = 17752, number of trials = 20000, p-value <
## 2.2e-16
## alternative hypothesis: true probability of success is not equal to 0.1666667
## 95 percent confidence interval:
##  0.8831411 0.8919459
## sample estimates:
## probability of success 
##                 0.8876