Question 5. [ 12 marks ] [Chapters 7 and 8] A study was conducted on customers of an Auckland cafe. The table below gives information on some of the variables collected: Variable Type Age group The age group of the customer (in years): 15 to 29, 30 to 44, 45 to 59, 60 to 74, 75 and over Coffee type The type of coffee ordered: fancy, not fancy Coffee time The time between ordering and receiving their coffee (in minutes) Food Whether the customer ordered food with their coffee: yes, no Food type The type of food ordered: counter, menu Food time The time between ordering and receiving their food (in minutes) Time The time the customer spends at the cafe (in minutes) (a) For each of the scenarios 1 to 4 below: [ 4 marks - 1 mark for each scenario ] (i) Write down the name of the variable(s), given in the table above, needed to examine the question. (ii) For each variable in (i) write down its type (numeric or categorical). (b) What tool(s) should you use to begin to investigate the scenarios 1 to 4 below? Write down the scenario number 1 to 4 followed by the appropriate tool. Hint: Refer to the blue notes in Chapter 1 in the Lecture Workbook. [ 4 marks - 1 mark for each scenario ] (c) Given that the underlying assumptions are satisfied, which form of analysis below should be used in the investigation of each of the scenarios 1 to 4 below? Write down the scenario number 1 to 4 followed by the appropriate Code A to F. [ 4 marks - 1 mark for each scenario ] Scenario 1 Is there a difference between the proportion of customers 15 to 29 years who ordered food with their coffee and the proportion of customers 75 years and over who ordered food with their coffee? Scenario 2 Does the time between ordering and receiving food depend on the type of food the customer orders? Scenario 3 Does the time between ordering and receiving coffee depend on the age of the customer? Scenario 4 Is the time between ordering and receiving fancy coffee different from that for coffee that is not fancy? Code | Form of analysis A One sample f-test on a mean One sample f-test on a proportion C One sample f-test on a mean of differences D Two sample f-test on a difference between two means /-test on a difference between two proportions One-way analysis of variance F-test