(a) Derive the (general) likelihood ratio test of homogeneity. The setup is exactly the same as the test of homogeneity for categorical data, the only difference is that we are deriving the LR test statistic instead of the Chisquared test statistic. (b) Calculate the likelihood ratio test statistic for the table below from the example we covered in the class. You should use R to do this. How does the test statistic compare to Pearson's chisquared statistic? Word Sense and Sensibility Emma Sanditon I Sanditon II a 147 186 101 83 an 25 26 11 29 this 32 39 15 15 that 94 105 37 22 with 59 74 28 43 without 18 10 10 4 Total 375 440 202 196