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Chapter 1: Problem 19

A Business Week North American subscriber study collected data from a sample of 2861 subscribers. Fifty-nine percent of the respondents indicated an annual income of \(\$ 75,000\) or more, and \(50 \%\) reported having an American Express credit card. a. What is the population of interest in this study? b. Is annual income a qualitative or quantitative variable? c. Is ownership of an American Express card a qualitative or quantitative variable? d. Does this study involve cross-sectional or time series data? e. Describe any statistical inferences Business Week might make on the basis of the survey.

Short Answer

Expert verified
a) North American Business Week subscribers. b) Quantitative. c) Qualitative. d) Cross-sectional. e) Predict trends or marketing strategies.

Step by step solution

01

Understanding the Population of Interest

The population of interest refers to the entire group of individuals or instances about whom we hope to learn. In this study, the population of interest is all North American subscribers to Business Week.
02

Classifying Annual Income

Annual income is a numerical value that can be measured, and it conveys how much an individual earns over a year. Therefore, annual income is a quantitative variable.
03

Classifying Ownership of American Express Card

Ownership of an American Express credit card is categorized by whether a subscriber possesses the card or not. This is a characteristic or attribute, which means it is a qualitative variable.
04

Identifying Type of Data in the Study

Cross-sectional data is collected at a single point in time, while time series data is collected over several time periods. Since the responses from subscribers were collected at one time, this study involves cross-sectional data.
05

Making Statistical Inferences

Statistical inferences might include generalizing the percentage of all subscribers who earn at least $75,000 annually or who own an American Express card, based on the sample data. Business Week might predict trends or marketing strategies for their services based on these inferential statistics.

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Key Concepts

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

Population of Interest
When we talk about the population of interest in statistical analysis, we mean the full group of people or objects we're curious about. In our study, this refers to all North American subscribers to Business Week. Imagine we have a big circle that includes all these subscribers. This is our target audience. By focusing on this group, Business Week aims to gain insights that reflect the broader trends among their subscribers. Understanding who the population of interest is helps researchers focus their data collection efforts effectively.
Quantitative Variable
A quantitative variable is all about numbers. It's something you can measure or count. In this study, the annual income of subscribers is a quantitative variable. Why? Because income is a number that shows how much someone earns over a year. Quantitative variables allow us to perform various mathematical computations, like finding averages or medians. This lets researchers draw meaningful conclusions from their data. They help paint a clearer picture of the patterns or behaviors in the population of interest.
Qualitative Variable
Qualitative variables describe qualities or categories rather than numbers. In our example, the ownership of an American Express card is a qualitative variable. It categorizes subscribers into groups: those who have the card and those who don鈥檛. These variables are crucial for understanding patterns in data that aren't related to numbers. They can point out trends in behaviors or preferences among specific groups within the population. Knowing who belongs to which category can help businesses tailor their services to meet the needs of different groups.
Cross-Sectional Data
Cross-sectional data refers to information collected at a single moment in time. Think of it as a snapshot capturing data from all the study's participants simultaneously. In this study, Business Week collected responses once from all subscribers. Using cross-sectional data allows researchers to understand the current state of the population of interest. Unlike time series data, which tracks changes over time, cross-sectional data gives a picture of a particular instance. This helps in making assessments about what is happening now, which can inform decision-making processes.
Statistical Inferences
Statistical inferences are drawn from sample data to make generalizations about the broader population. For Business Week, this means taking the survey results and applying them to all North American subscribers. These inferences can reveal how many subscribers probably earn over $75,000 or own an American Express card. By understanding these trends, Business Week might adjust marketing strategies to better cater to their audience. Statistical inferences help convert data into actionable insights that influence real-world decisions.

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Most popular questions from this chapter

A survey of 131 investment managers in Barron's Big Money poll revealed the following \((\text {Barron's,} \text { October } 28,2002)\) \(43 \%\) of managers classified themselves as bullish or very bullish on the stock market. The average expected return over the next 12 months for equities was \(11.2 \%\) \(21 \%\) selected health care as the sector most likely to lead the market in the next 12 months. When asked to estimate how long it would take for technology and telecom stocks to resume sustainable growth, the managers' average response was 2.5 years. a. Cite two descriptive statistics. b. Make an inference about the population of all investment managers concerning the average return expected on equities over the next 12 months. c. Make an inference about the length of time it will take for technology and telecom stocks to resume sustainable growth.

The Commerce Department reported receiving the following applications for the Malcolm Baldrige National Quality Award: 23 from large manufacturing firms, 18 from large service firms, and 30 from small businesses. a. Is type of business a qualitative or quantitative variable? b. What percentage of the applications came from small businesses?

State whether each of the following variables is qualitative or quantitative and indicate its measurement scale. a. Annual sales b. Soft drink size (small, medium, large) c. Employee classification (GS 1 through GS18) d. Earnings per share e. Method of payment (cash, check, credit card)

Columbia House provides CDs to its mail-order club members. A Columbia House Music Survey asked new club members to complete an 11 -question survey. Some of the questions asked were: a. How many CDs have you bought in the last 12 months? b. Are you currently a member of a national mail-order book club? (Yes or No) c. What is your age? d. Including yourself, how many people (adults and children) are in your household? e. What kind of music are you interested in buying? Fifteen categories were listed, including hard rock, soft rock, adult contemporary, heavy metal, rap, and country. Comment on whether each question provides qualitative or quantitative data.

The marketing group at your company developed a new diet soft drink that it claims will capture a large share of the young adult market. a. What data would you want to see before deciding to invest substantial funds in introducing the new product into the marketplace? b. How would you expect the data mentioned in part (a) to be obtained?
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