2.3

## Deakin University

How would you encourage people to carpool?

# Statistical solutions

To solve problems and test hypotheses, we often need to know how widespread something is and how it is related to something else.

In the last step, we asked how you could figure out how likely people are to share a ride to work if they live together and if there’s anything you could do to predict this.

Throughout the rest of the step, you’re going to take a look at one possible solution to this problem. Throughout the rest of Week 2, we’ll show you how you could put the kind of solution we’re proposing into action.

### Hypothesis

In this solution, the first step is to create a hypothesis, as follows: that as the number of residents eligible for a driver’s licence residing in a dwelling increases, the number of cars used for transit to work also increases.

If it turns out the opposite is true, we’d know that people are already carpooling or using other modes of transport; useful information, even if it means we were wrong.

To test the hypothesis, you could take a sample of the overall population. You could, perhaps, send a survey to households in your neighbourhood, asking residents a few questions about how many people in the house have a driver’s licence, travel regularly to work and whether or not they share a car.

### Proportion and distribution

Once the results were in, we’d need to work out how typical it is to share a ride to work. We need distribution and proportion to show us that.

Using this data, we could build a picture of:

• the number of licenced drivers in each household and cars taken to work each day and their distribution (by distribution we mean that, for example, 26 households who responded to the survey take three separate cars to work on a normal workday, 14 took four and so on)
• the proportion (or percentage) of households this represents
• the average number of licenced drivers and cars taken to work each day per household.

Once you know this, you’re also going to have all the information you need to figure out how likely a household is to be an ‘average household’ and how closely our sample’s average is to that of the entire population.

This can be determined using standard deviation and confidence intervals, both of which we’ll look at in detail later in the week.

### Correlation

Finally, we still need to figure how closely related the number of licenced drivers per household is to the number of cars taken to work each morning.

If the number of licence holders and the number of cars typically taken to work goes up and down together, you’d be able to infer two things:

• the more licences, the more cars taken to work
• living in the same house doesn’t influence how likely people are to carpool.

You may want to control against a number of factors including age, employment status or whether or not the members of the household were related to each other.

Once you were confident of your results, you’d need to figure out what to do with them.