PLEASE PROVIDE ALL DETAILS A car company conducted a study t

PLEASE PROVIDE ALL DETAILS. A car company conducted a study to understand the relationship between age groups and drivers\' primary vehicles. (Their primary vehicle is the single vehicle that they drive most often.) Selecting and contacting a random sample of 350 drivers, the company compiled the results of their data collection in the following table.

Station Wagons & Vans

Sedans

Sports & SUV’s

Other

Less than 35

17

34

22

11

36 thru 55

46

49

40

15

56 and above

32

61

16

7

1. Does is seem likely that the two events, selecting an older driver (56 and above) and selecting Station Wagon/Van driver, are independent events? PLEASE EXPLAIN IF INDEPENDENT EVENTS

2. Of the 12 sub-categories in the above table, which pairs are mutually-exclusive. Explain how you arrived at your answer.

PLEASE IDENTIFY ALL PAIRS IN NUMBER 2

Solution

a)

Probability of all drivers choosing a station wagon or van = 0.271

Probability of an older driver choosing a SW or van = 32/(61+16+32+7) = 0.276

Since the probabilities are approximately same, hence we can say that it looks like they are independent events

b)

All the pair of car types are mutually exclusive

4C2 = 6 combinations = (SW,sedan), (SW,sports), (SW,others) and remaining three pairs

Age groups are mutually exclusive 3C2 = 3 pairs