

In [1]:

    
x <- c(315,101,108,32)
n <- sum(x)

a)



In [2]:

    
p0 <- c(9,3,3,1)/16
chisq.test(x, p=p0)









    Out[2]:





	Chi-squared test for given probabilities

data:  x
X-squared = 0.47002, df = 3, p-value = 0.9254

b)



In [3]:

    
L0 <- dmultinom(x, prob=p0)
Lhat <- dmultinom(x, prob=x/n)
(Lamb <- -2*log(L0/Lhat))
pchisq(Lamb, df=3, lower.tail=FALSE)









    Out[3]:




0.475445238998873






    Out[3]:




0.924251903974394



In [4]:

    
dchisq(0.95, df=1)









    Out[4]:




0.254541374114313