A National Highway Traffic Safety body is concerned about the fire hazards posed by vehicles involved in different types of collisions. They collate information of past accidents involving vehicle fires, including the type of car (electric vs petrol) and the type of collision (front collision vs rear collision). They construct the following contingency table from a random sample: Accident type Front Collision Rear Collision Type of vehicle Petrol 24 30 Electric 24 13 What is the total sample size? The next question uses information provided in this question. 12 pts"Ansh's iPhone"? D Question 4 12 pts (a) Using the contingency table find each of the following probabilities and state how we interpret these probabilities: P(Front Collision) P(Petrol | Front Collision) (3 marks) (b) Which test statistic should be used to test whether there is a relationship between the accident type and the type of vehicle? Provide the null and alternative hypothesis, state the appropriate test statistic and its distribution; and describe the appropriate decision rule (you are not required to do the test, you will be asked to do this in part b and c). (2 marks) (c) Are you required to make any assumptions to use the test you have proposed in part (a) above? If so, what is the assumption, or what are those assumptions? Now check any assumption or assumptions you are making. (3 marks) Hint: Rather than do calculations manually, you can use excel to do the necessary calculations and present the formula you used alongside your results (d) Regardless of your conclusions in part (b), now implement the test you have chosen in part (a), using a 5% level of significance. (4 marks) Edit View Insert Format Tools Table . . . B IYA & T V 12pt Paragraph