3. McCullagh and Nelder discuss an experiment concerning the effect on taste of four cheese additives, names A, B, C, and D. To this end, several tasters are given samples with each additive and evaluate their taste in a nine-point "hedonic" scale ranging from I, 'strong dislike', to IX, excellent taste'. To analyze the experiment data we fit a proportional odds model and obtain the following results: Call : polr (formula = taste ~ cheese, data = cheese, weights = y) Coefficients : cheeseB cheeseC cheeseD -3. 351849 -1.709903 1. 612780 Intercepts : I| II II | III III | IV IVIV VIVI VI | VII -5. 46737764 -4.41220880 -3.31263651 -2. 24401365 -0.90776781 0. 04426294 VIII VIII VIII| IX 1 . 54593422 3. 10579153 Null Deviance: 859. 8018 Residual Deviance: 711.3479 (a) Interpret the coefficient cheeseB in terms of odds ratios. How should the cheese additives be ordered relative to taste, from best to worst? Explain. (b) What is the estimated probability that additive A gets at most a tasting of IV? (c) Do the additives in the experiment really taste different? Conduct a likelihood ratio test to assess indifference to additives; state the test statistic, its distribution under the null and your assumptions. What is your conclusion