34. Using the data in the Excel file Consumer Transportation Survey, develop a c

Question

34. Using the data in the Excel file Consumer Transportation Survey, develop a contingency table for Gender and Vehicle Driven then convert this table to a joint proba- bility distribution and compute marginal probabilities. a. What is the probability that a respondent is male b. What is the probability that a female respondent c. If it is known that an individual drives a car, what is d. If it is known that an individual is female, what is e. Determine whether the random variables "gender" pendent. What would this mean for advertisers? and drives a minivan? drives either a truck or an SUV the probability that the individual is male? the probability that she drives an SUV? and the event "vehicle driven" are statistically inde-

Explanation / Answer

The contingency table is as follows:

a. P(male and minivan)=26/59*10/59 [if two events A and B are disjoint, then P(A and B)=P(A)*P(B)]

=0.0747

b. P(female driving truck or female driving SUV)=4/14+8/14 [if two events C and D are disjoint, then P(C or D)=P(C)+P(D)]

=0.8571

c. Use information directly from table. P(male|car)=6/20=0.3

d. Use information from table directly. P(SUV|female)=8/33=0.2424

Female Male Total Truck 4 8 12 SUV 8 9 17 Minivan 7 3 10 Car 14 6 20 Total 33 26 59

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