# Application Exercises

## Exercise 1: Predicting Group Wealth

Wealth is normally distributed, or is it? Ask one individual in your group to disclose the amount of cash he or she is carrying, then ask group members how confident they are that this amount represents the group average. Ask a second individual, a third, and so on, recording each dollar amount from lowest to highest. As you record each new amount, calculate and record the mean value for the group, as shown in Exhibit 8.1. At what point does your group start to become confident about predicting the group average?

No cash? Try the same exercise with routine expenditures, for example daily expenditures on coffee or lunch, monthly expenditures on entertainment or transport, or annual expenditure on clothing.

## Exercise 2: Generalizing from a Sample to a Population

Assume that the group you did Exercise 1 with is randomly selected from a wider student population. Use the formula for standard deviation to calculate the probabilities that the mean value for wealth you calculated from Exercise 1 will be found in that population.

## Exercise 3: Occupation and Beverage Preferences

Back to the coffee bar. What test would you use to help decide whether beverage preferences are related to occupation—more specifically, whether faculty and students differ significantly in their drink preferences?

Hint 1: You will be dealing with two categorical variables here—occupation and type of beverage.

Hint 2: Before you can develop a table that sets out your data, you will first need to make a decision about how you will categorize beverages. For example, would tea, coffee, soda, and water be an appropriate set of categories, or would cappuccino, latte, espresso, and Americano best capture your group’s preferences?

Note also that here we can make a reasonable guess about direction of causality. Coffee drinking has many documented physiological effects, but, to date, demonstrable change in occupation is not one of them. If you find a significant difference between faculty and students in beverage preferences, it would be reasonable to assume that these preferences are predicted by occupation rather than vice versa.

## Exercise 4: “The Internet of Things” Revisited

Revisit Exercise 3, “The Internet of Things,” from Chapter 7. Here, you were capturing responses to statements about the Internet of Things using Likert-type response options. Now you are in a position to compute the standard deviation for the responses you captured to each statement. What is the 95% confidence interval for the mean value of the responses you obtained to each question?