Homework 14: Conduct a simulation study in R to confirm the null distribution
of the chi-square test of homogeneity by doing the following:
1. Draw two multinomials of size n1=873 and n2=624 from p=((.302,.566,.091,.041))
2. Compute chi-square test statistic for homogeneity
3. Repeat 10000 times
4. Compare histogram with the pdf of chi-square with  3 df

Below is portion of R session to start you out. 

*****************************************************************
> p<-c(.302,.566,.091,.041)
> p
[1] 0.302 0.566 0.091 0.041

> x<-rmultinom(10,873,p)   #### 10 reps of x-sample
> x
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]  253  267  259  242  241  249  255  277  259   261
[2,]  508  503  493  516  505  492  501  483  511   487
[3,]   86   77   84   80   89   92   79   72   78    88
[4,]   26   26   37   35   38   40   38   41   25    37

> y<-rmultinom(10,624,p)   #### 10 reps of y-sample
> y
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]  178  175  194  180  174  207  182  187  175   210
[2,]  374  366  337  355  377  349  363  350  346   327
[3,]   51   60   64   65   49   45   57   63   68    69
[4,]   21   23   29   24   24   23   22   24   35    18

> xy<-cbind(x[,1],y[,1])   #### Calculate chi-square test-statistic for first columns
> chisq.test(xy)$statistic
X-squared 
 1.507721