1. Do cat owners sleep better than those without cats? To help answer this question, a cat enthusiast obtained a random sample of 500 Canadians, each of whom answered two questions: 1. do you have a cat? (yes or no], 2. How well do you sleep? (good, neutral, bad). The dataset "CatSleep.xIsx" contains her findings R X Cat Sleep ) Complete the contingency table by hand and then check your answer by generating a two-way table in R. (3 marks) Good ($,) Neutral ($,) Bad (S.) Total Cat (C) 58 70 190 No Cat (C2) 67 168 75 Total 137 500 Use the frequency table from (a) estimate the following probabilities. b) Find the probability that a randomly selected Canadian is a good sleeper. (2 marks) c) Find the probability that a randomly selected Canadian is a bad sleeper and a cat owner. (2 marks) d) Find the probability that a randomly selected Canadian is a neutral sleeper or a cat owner. (3 marks) e) Find the probability that a randomly selected non-cat owner is a bad sleeper. That is, find the probability that a randomly selected Canadian is a bad sleeper, given they are not a cat owner (3 marks) f) Find the probability that a randomly selected bad sleeper is not a cat owner. (3 marks) g) Are events Cz and 53 independent? Explain your answer. (2 marks) h) Are events C and $3 mutually exclusive? Explain your answer. (2 marks)