Problem_9_11_39.r

# Problem 9_11_39.r

data.table<-data.frame(
  days=c(3,3,3,3,3,3,3,3,3,2),
  bites=c(137,150,163,201,269,155,142,146,148,110)
)

# Compute the bites per day for each period
x.bitesPerDay=data.table$bites/data.table$days

# Plot the rate
plot(x.bitesPerDay)

# There is a peak rate at the period containing day 29 (period 5)

# Optional: conduct a chi-square goodness of fit test

average.bitesPerDay=sum(data.table$bites)/sum(data.table$days)

expected.bitesPerPeriod=data.table$days*average.bitesPerDay

chisq.table<-cbind(
  data.table, expected=expected.bitesPerPeriod,
  chisqj= ((data.table$bites - expected.bitesPerPeriod)^2)/(expected.bitesPerPeriod))

print(chisq.table)

##    days bites expected      chisqj
## 1     3   137 167.6897  5.61665497
## 2     3   150 167.6897  1.86608947
## 3     3   163 167.6897  0.13115219
## 4     3   201 167.6897  6.61686060
## 5     3   269 167.6897 61.20703128
## 6     3   155 167.6897  0.96027002
## 7     3   142 167.6897  3.93559389
## 8     3   146 167.6897  2.80542733
## 9     3   148 167.6897  2.31190481
## 10    2   110 111.7931  0.02876045

print(apply(chisq.table,2,sum))

##       days      bites   expected     chisqj 
##   29.00000 1621.00000 1621.00000   85.47975

pValue=1-pchisq(sum(chisq.table$chisqj), df= (10 -1 -1))
print(pValue)

## [1] 3.885781e-15