There is typically a question (six sub-questions) related to risk, using two-way tables. These questions lead to investigations using absolute risk and relative risk, and assessing the validity of statistical claims.
In these practice exams, it is Question Two.
The café Dolce Forte sometimes has drinks returned by customers.
Alexa (a new staff member) and Oscar (a very experienced staff member) keep track of how many drinks they have had returned in the first week Alexa is employed.
(a) Calculate the percentage of drinks made by Alexa or Oscar that were returned this week.
(b) Calculate the proportion of Oscar’s coffees that were not returned.
(c) Calculate the proportion of returned coffees that are made by Alexa.
(d) If Oscar makes two coffees, what is the probability that neither of these coffees are returned?
(e) The manager of Dolce Forte calls Alexa into her office. She claims that Alexa is three times more likely to prepare a coffee that is returned, compared to experienced staff like Oscar.
Investigate the validity of the manager’s claim.
(f) Oscar also keeps track of the number of coffees returned and whether or not that coffee contains milk.
Oscar made 1422 coffees, of which 989 contained milk (such as a latte or flat white). The remaining coffees had no milk (such as a long black or short black), and of these 14 were returned.
Oscar claims that customers at Dolce Forte are more likely to return a coffee if it has no milk. Investigate the validity of this claim.