Given that a population of a certain area has been classified according to the n

Question

Given that a population of a certain area has been classified according to the number of cars owned, and given that there are only two transportation options available (drive or take the bus). Now assume the population distribution is as follows: Consider a stratified sample with 40% households having 2+ cars, and 60% having 1 or 0 cars, calculate the corresponding table of probabilities for the stratified sample. Consider a choice-based sample with the following distribution for Drive, Take the Bus, and Ride the Metro: 60%, 25%, 15%, respectively, determine the corresponding table of probabilities for the choice-based Sample For the stratified and choice-based sample, determine the probability of a member of a household with 2+ cars driving.

Explanation / Answer

1. The Excel formulas for the stratified probabilities is given below:

The key idea is to distribute the probabilities of 0.4 and 0.6 for the respective 2+cars/household and 1 or 0 car/household according to the distribution given in the data.

2) For the choice-based sample, we now look at row probabilities instead of the column probabilities and recalculate the probabilities in Excel as follows:

3) From the table given in 1), the probability of a member of a household with 2+cars driving in the stratified sample is 0.2667, while for the same in choice-based sample, the probability is given by the table in 2) as 0.52.

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