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Chapter 1: Problem 1

For the situations described. (a) What are the cases? (b) What is the variable and is it quantitative or categorical? People in a city are asked if they support a new recycling law.

Short Answer

Expert verified
The cases in this context are the individuals in the city who get questioned. The variable in this exercise is the response of individuals to the question of whether they support a new recycling law or not. This variable is categorical, not quantitative.

Step by step solution

01

Identify the Cases

The 'cases' in this scenario represent the individual units we're studying. In this particular exercise, the question is asked to 'people in a city', which means every single person being questioned about the recycling law is a case.
02

Identify the Variable

A variable is any characteristic that can differ among individuals. In this context, the variable to be measured is whether or not an individual supports a new recycling law.
03

Classify the Type of Data

We need to determine whether the variable is quantitative or categorical. The response to the question (either 'yes' they support the new recycling law, or 'no' they do not) is not a numerical measurement, rather it is a category. Therefore, the data collected for this variable is considered to be categorical.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Cases
In statistics, cases refer to the individual units that are being observed or studied in a given scenario. Think of them as the participants or subjects from whom data is collected. Take, for example, a survey conducted among city residents to gauge their opinion on a new recycling law. Every person who participates in this survey is referred to as a 'case'.

Here are some key points about cases:
  • Cases are often individuals, but they can also be entities like companies, countries, or events.
  • In our recycling law scenario, each person surveyed represents one case.
By identifying cases, we establish the units of observation and understand whose responses or characteristics are being analyzed. This forms the foundational step in structuring any statistical investigation.
Exploring Variables
Variables are integral in statistics as they represent the characteristics or attributes of cases that are studied. They can vary from one case to another, hence the name 'variable'. In the context of our scenario where a city surveys people about a recycling law, the variable is the opinion each person has鈥攚hether they support or oppose the law.

Here's what you need to know about variables:
  • They can be reflective of opinions, measurements, quantities, among other things.
  • Variables can be either quantitative or categorical. Quantitative variables involve numerical data, like height or weight, whereas categorical variables involve descriptive data, like gender or preference.
  • In our scenario, the variable asks if each person supports the recycling law, which does not result in a numerical output but in a category (support/oppose).
Understanding what constitutes a variable helps in determining how to collect and analyze data effectively.
Grasping Categorical Data
Categorical data encompasses information that can be categorized into distinct groups or labels, without involving any notion of quantity or numerical values. In the recycling law survey, the response to whether a person supports the law or not is a perfect example of categorical data.

Consider these important aspects of categorical data:
  • Categorical data represents characteristics and traits like color, type, gender, or preference.
  • Responses that categorize into groups like yes/no, agree/disagree are classic examples.
  • In our scenario, the data collected is purely categorical because it captures the preference (support or opposition) of each respondent towards the law.
Categorical data is crucial for understanding distributions, frequencies, and trends within groups, helping in decisions and policy-making processes. Understanding this type of data also aids in determining the right statistical methods for analysis.

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Most popular questions from this chapter

In Exercise \(1.18,\) we ask whether experiences of parents can affect future children, and describe a study that suggests the answer is yes. A second study, described in the same reference, shows similar effects. Young female mice were assigned to either live for two weeks in an enriched environment or not. Matching what has been seen in other similar experiments, the adult mice who had been exposed to an enriched environment were smarter (in the sense that they learned how to navigate mazes faster) than the mice that did not have that experience. The other interesting result, however, was that the offspring of the mice exposed to the enriched environment were also smarter than the offspring of the other mice, even though none of the offspring were exposed to an enriched environment themselves. What are the two main variables in this study? Is each categorical or quantitative? Identify explanatory and response variables.

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