Question 4. Part A: Ontario's Alpine Skiers An alpine ski coach in Ontario wants insight on how alpine skiers from the province are per forming in the Slalom, Giant Slalom, and Super G events in national competitions. A random sample of 74 Ontario alpine skiers who completed in the Canada Winter Games between 1983 and 2015 is selected. The following table summarizes the places in which alpine skiers nish in each of the three events. This table can be found in the Excel sheet Ontario and Quebec. Place #1 to #3 (Medals) Place #4 to #10 Remaining Places Slalom 3 10 11 Giant Slalom 5 9 16 Super G 4 8 8 (i) If an Ontarian alpine skier is chosen at random, what is the probability that they received a medal in their event? (ii) If an Ontarian alpine skier who finished a Slalom is chosen at random, what is the proba- bility that they placed in the top 10? (iii) Test at the 5% significance level the claim that finishing place is independent of event. (Hint: Use the test of independence.) Do Ontarian alpine skiers appear to be better at certain events than other events? Explain. (iv) Use the stacked bar graph below along with the result in part A. (iii) to describe the perfor- mance of Ontario's alpine skiers in national competitions. (Hint: Look at the distribution of proportions of individual event results.) Places for Ontario's Alpine Skiers by Event 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Slalom Giant Slalom Super G Proportion of Skiers who Placed #1 to #3 Proportion of Skiers who Placed #4 to #10 Proportion of Skiers in Remaining PlacesPart B: Quebec's Alpine Skiers A Quebecois alpine ski coach also wants to perform the same analysis for the province's alpine skiers. A random sample of 72 alpine skiers from Quebec were selected from the 1983 to 2015 Canada Games. The following table summarizes the places in which alpine skiers nish in each of the three events. This table can be found in the Excel sheet Ontario and Quebec. Place #1 to #3 (Medals) Place #4 to #10 Remaining Places Slalom 7 10 4 Giant Slalom 2 14 9 Super G 4 7 15 (i) If a Quebecois alpine skier who nished a Slalom is chosen at random, What is the proba bility that they placed in the top 10? Compare this result with the sample probability you obtained in part A.(ii). for Ontarian alpine skiers. Based on this comparison, could you conclude that the population proportion of Ontarian alpine skiers who place in the top 10 of Slalom is different from the population proportion of Quebecois alpine skiers who place in the top 10 of Slalom? Explain why or why not. (ii) Construct a stacked bar graph like the one in part A.(iv), using the data for Quebec's alpine skiers. (Hint: Create a 100% Stacked Column graph in Excel and ensure the legend is descriptive.) (iii) After examining the bar graph in part B.(ii), do you believe that finishing place is inde- pendent of event for Quebecois alpine skiers? Explain. (iv) Test at the 5% significance level the claim that finishing place is independent of event. (Hint: Use the test of independence.) Do Quebecois alpine skiers appear to be better at certain events than other events? Explain. (v) Using your results from the bar graph and hypothesis test, describe the performance of Quebec's alpine skiers in national competitions. Describe to the Quebecois coach how these results can help inform their training decisions