In: Statistics and Probability
Imagine that you are the Mayor of a city, and you want to know who would benefit the most from a new program encouraging hiking on the trails throughout the parks in the city. You have some limited city funds to allow your city manager to field a survey of 100 families, with a sample designed to be representative of the city population. What two groups (i.e. two categories in the same nominal or ordinal variable) would you be interested in seeing whether they vary on the mean number of minutes they currently hike in the parks? Examples of variables from the survey could be age groups, racial or ethnic groups, income groups, different health statuses...there are many options. Describe your two groups from the same nominal variable that you would want to compare, and why that would be useful information to inform how to best create your new hiking program.
I think that a good option is to create groups based on age. For example, one group could be represented by people under the age of 30 years old and the other group by people who are at least 30 years old.
The choice to take the ordinal variable “Age” as a grouping factor is because I think that the use of the trails can depend a lot on the age of the people.
Young people (under the age of 30) may use the trails for jogging, and if so, they are unlikely to use the trails for more than 20 minutes a day. In contrast, people 30 years of age or older are likely to be people with established families and use the trails for walks with their family members and therefore their duration on the trails for one day may be longer.
But on the other hand, young people are also likely to use the trails more frequently than adults, for example in a week, as it is reasonable that they have more time to do so.
In any case, if the mayor's idea is to encourage the use of trails, he can make a study to see if one of the two groups uses trails less and take measures based on the response obtained in the study. For example, if it turns out that young people use the trails the least and you want to increase that frequency, you can apply policies such as expanding the trails to facilitate exercise.