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Question: a simple random sample of 227 university students were asked...

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 A simple random sample of 227 university students were asked what pasta they usually order and with which sauce. The preferences of these respondents are summarised below: 

      Sauce  
Pasta  Bolognese Carbonara Pesto Total 
Spaghetti 30  20  10  60
Gnochhi 40 30 25 95
Ravioli 22 25 25 72
Total  92 75 60 227

(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? (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 Gnocchi? (2 Marks)

ii. What is the probability that a respondent prefers Spaghetti and Bolognese sauce? (3 Marks)

iii. What is the probability that a respondent prefers Ravioli or Carbonara sauce? (3 Marks)

iv. Suppose the preferred sauce is Pesto. What then is the probability the pasta ordered is Ravioli? (3 Marks)

v. Suppose that the preferred Pasta is Spaghetti. What then is the probability the sauce ordered is Bolognese? (3 Marks)

(c) Are the events Gnocchi and Sauce statistically independent or dependent? How do you know? Show all calculations that support your answer. (7 Marks)

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