hw stat

##10.3.7
hospital = read.table("ds10.3.7-hospital-emergency-room.txt", header = T)
#n is the sample size
n = sum(hospital$Frequency)
#This creates a vector (x) of the numbers 0 to 12 
x = seq(0:12)-1
#Probabilities calculated - creates a vector with all of them in there. 
probs = dpois(x,7)
#Last entry in probs vector is for anything greater than 13
probs[14] = 1-(ppois(12,7))
#Check that probabilites sum to 1. 
sum(probs)
#vector expected values (exp). probabilities * sample size
exp = probs*n
#view expected values
exp
#observed values (obs): read straight from the table
obs = hospital$Frequency
#Calculate X2 (chi-square) statistic
X2 = ((obs-exp)^2)/exp
X2 = sum(X2)
#calculate p-value
pchisq(102.3199,13, lower.tail = F)