1. a) b) c) d) e) f) g h) An analyst would like to determine if there is an association between the highest academic degree of an individual and preferred social media platform. A simple random sample of 780 people provides the data shown below. (23 marks) Facebook | YouTube | WhatsApp | Instagram Associate degree 50 ' 105 55 35 245 Bachelor's degree 60 ' 100 65 40 265 70 80 75 45 Master's degree Provide a description of the side-by-side bar graph. (2 marks) 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% M Associate degree M Bachelor's degree Percentage M Master's degree Facebook YouTube WhatsApp Instagram Calculate the expected frequency of the cell \"bachelor's degree and Facebook\" and interpret this value in the context of the question. (3 marks) Suppose the value of chi-square statistic is 10.026. Is there sufficient evidence for the analyst to conclude that an association exists between the highest academic degree of an individual and preferred social media platform? Show all steps of a chi-square test and use an appropriate decision point to support your conclusion. (3 marks) Suppose one person is randomly selected from the study. What is the probability that the person does not prefer Instagram? (1.5 marks) Suppose one person is randomly selected from the study. What is the probability that the person has a bachelor's degree and prefers Facebook? (1.5 marks) Suppose one person is randomly selected from the study. What is the probability that the person has a master's degree or prefers Instagram? (2 marks) Suppose a randomly selected person has a bachelor's degree. What is the probability that this person prefers YouTube? (2 marks) Suppose a randomly selected person prefers WhatsApp. What is the probability that this person has an associate degree? (2 marks) Suppose one person is randomly selected from the study. Are the events 4 = {the person has an associate degree} and B = {the person prefers YouTube} mutually exclusive? Justify your answer using probability. (2 marks) a) b) Suppose one person is randomly selected from the study. Are the events 4 = {the person has a bachelor's degree} and B = {the person prefers Facebook} independent? Justify your answer using probability calculations. (2 marks) If two people are randomly selected from the study, what is the probability that they both prefer Instagram? (2 marks) A market researcher wishes to compare the proportions of homes with air conditioning among communities. Eighty homes were randomly selected from each community, and the results are shown below. If the value of is 8.9732, is there sufficient evidence for the market researcher to conclude that a difference exists in the proportions of homes with air conditioning among the communities? Show all steps of a chi-square test and use an appropriate decision point to support your conclusion. (3 marks) Total Yes 128 No 112 Total 240 At a fast-food restaurant, the probability that a customer orders a hamburger is 0.63, the probability that a customer orders French fries is 0.58, and the probability that a customer orders a hamburger and French fries is 0.47. (4 marks) Let A be the event that a customer orders a hamburger and B be the event that a customer orders French fries. Draw a Venn diagram and label it with probabilities. (2 marks) If a customer orders a hamburger, what is the probability that the customer also orders French fries? Give your answer to four decimal places. (2 mark)