Question Cine (5 marks each it} Marks) A midway game called \"Crowns and Anchors\" has sir: symbols that you can bet $1 on. A wheel is spun, and you receive $1 for each corresponding symbol in the segment that turns up on the spin. The wheel has 29 equal segments, and each segment contains 3 symbols. For each symbol, for example vs, one segment contains 3 1!, two segments contain 2 1 {plus some other symbol], and three segments contain 1 it [plus two other symbols). Thus 14 segments will have other symbols and contain no vs. a) If you bet $1 on v, what is your expected win per play? b) 1Would you play this game? 1Why do people buy lottery tickets? Question Two (4 marks each 2:1 marks] Answer the following questions for the GreatCuppa data seL ssume that the sample of 259 customers is a random sample from the population of all customers. a) Use the 'Data I Data nalysis' tool to calculate descriptive statistics for the cups per week consumed by the surveyed customers. There is a discrepancy between the median and mean cups per week for these data. Use a histogram to explain this. b) Calculate a 9591':- confidence interval for the mean income of all customers whose favourite coffee is Latte. c) Calculate a 99% confidence interval for the W of customers who prefer cappuccino. d) Calculate a 95% confidence interval for the mean income of all customers who prefer 'other'. e) John rabica has suggested GreatCuppa customers who prefer regular coffee are in a mid to lower income bracket (less than $59,999). You are not; willing to accept John's opinion unless you have strong evidence supporting him. Conduct an appropriate test of hypothesis at the 5% level of signicance. Give a clear conclusion regarding John's speculation. a) John believes that Greatcuppa appeals equally to married and single customers. Conduct an appropriate test of hypoiesis. Be sure to state any assumptions required for your test and give a clear conclusion. Question Three (3 marks each 16 marks)