A simple random sample of 220 university students were asked what pasta they usually order and with which sauce. The preferences of these respondents are summarised below: Sauce Bolognese Pasta Spaghetti Gnocchi Carbonara Pesto Total 32 25 11 68 38 26 24 88 Ravioli 18 23 23 64 Total 88 74 58 220 (a) Use Excel to obtain a 100% stacked column chart for the data from the table. What does your chart suggest between the relationship between Pasta and Sauce? EXCEL Instructions: Refer to Topic 6 in the Excel Booklet for instructions on how to obtain 100% stacked column chart. (b) Use the contingency table to calculate the following probabilities; include an appropriate probability statement for each case: i. What is the probability that a respondent prefers Spaghetti? ii. What is the probability that a respondent prefers Gnocchi and Carbonara sauce? iii. What is the probability that a respondent prefers Ravioli or Pesto sauce? iv. Suppose the preferred sauce is Bolognese. What then is the probability the pasta ordered is Spaghetti? Suppose that the preferred Pasta is Ravioli. What then is the probability the sauce ordered is Carbonara? V. (c) Are the events Spaghetti and Sauce statistically independent or dependent? How do you know? Show all calculations that support your answer.