2. (8 points) The table below displays primary food choice for a sample of alligators, classied by length (22.3 meters, >23 meters) and by the lake in Florida in which they were caught. Primary food choice Lake Size Fish Invertebrate Reptile Bird Other Hancock 32.3 25 4 2 2 8 >2.3 8 0 1 3 5 Oklawaha 32.3 6 1 1 1 O 3 >2.3 15 8 6 1 0 Trafford 32.3 5 1 1 2 1 5 >2.3 10 7 6 3 5 George $2.3 18 19 1 2 3 >2.3 20 1 0 1 3 (a) (2 points) Fit a model to describe effects of length and lake on primary food choice. Report the prediction equations. (1)) (2 points) Obtain the Wald condence intervals for the effects of length. (c) (2 points) Using the t of your model, estimate the probability that the primary food choice is sh, for each length in Lake Oklawaha. Interpret the effect of length. (d) (2 points] Conduct a Pearson's chisquared test of goodness of t. Interpret