Chapter 1: Q3. (page 49)
List and define the four elements of a descriptive statistics problem.
Short Answer
Sample size, variables required, numerical summary tools, and conclusions are the four elements of a descriptive statistics problem.
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Chapter 1: Q3. (page 49)
List and define the four elements of a descriptive statistics problem.
Sample size, variables required, numerical summary tools, and conclusions are the four elements of a descriptive statistics problem.
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Stock prices. As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. They were then asked to summarize the current prices (also referred to as the closing price of the stock for a particular trading date) of the collected stocks using graphical and numerical techniques.
a. Identify the population of interest for this study.
b. Is the variable being collected quantitative or qualitative?
c. Identify the data collection method used in this study.
d. Identify the sample of interest for this study.
e. Identify the experimental unit and variable of interest for this study.
Corporate sustainability and firm characteristics. Corporate sustainability refers to business practices designed around social and environmental considerations (e.g., "going green"). Business and Society (March 2011) published a paper on how firm size and firm type impact sustainability behaviors. The researchers added questions on sustainability to a quarterly survey of Certified Public Accountants (CPAs). The survey was sent to approximately 23,500 senior managers at CPA firms, of which 1,293 senior managers responded. (Note: It is not clear how the 23,500 senior managers were selected.) Due to missing data (incomplete survey answers), only 992 surveys were analyzed. These data were used to infer whether larger firms are more likely to report sustainability policies than smaller firms and whether public firms are more likely to report sustainability policies than private firms.
a. Identify the population of interest to the researchers.
b. What method was used to collect the sample data?
c. Comment on the representativeness of the sample.
d. How will your answer to part c impact the validity of the inferences drawn from the study?
Treasury deficit prior to the Civil War. In Civil War History (June 2009), historian Jane Flaherty researched the condition of the U.S. Treasury on the eve of the Civil War in 1861. Between 1854 and 1857 (under President Franklin Pierce), the annual surplus/deficit was +18.8, +6.7, +5.3, and +1.3 million dollars, respectively. In contrast, between 1858 and 1861 (under President James Buchanan), the annual surplus/deficit was -27.3, -16.2, -7.2, and -25.2 million dollars, respectively. Flaherty used these data to aid in portraying the exhausted condition of the U.S. Treasury when Abraham Lincoln took office in 1861. Does this study represent a descriptive or inferential statistical study? Explain.
Monitoring product quality. The Wallace Company of Houston is a distributor of pipes, valves, and fittings to the refining, chemical, and petrochemical industries. The company was a recent winner of the Malcolm Baldrige National Quality Award. One of the steps the company takes to monitor the quality of its distribution process is to send out a survey twice a year to a subset of its current customers, asking the customers to rate the speed of deliveries, the accuracy of invoices, and the quality of the packaging of the products they have received from Wallace.
a. Describe the process studied.
b. Describe the variables of interest.
c. Describe the sample.
d. Describe the inferences of interest.
e. What are some of the factors that are likely to affect the reliability of the inferences?
Drafting NFL quarterbacks. The National Football League (NFL) is a lucrative business, generating an annual revenue of about $8 million. One key to becoming a financially successful NFL team is drafting a good quarterback (QB) out of college. The NFL draft allows the worst-performing teams in the previous year the opportunity of selecting the best quarterbacks coming out of college. The Journal of Productivity Analysis (Vol. 35, 2011) published a study of how successful NFL teams are in drafting productive quarterbacks. Data were collected for all 331 quarterbacks drafted between 1970 and 2007. Several variables were measured for each QB, including draft position (one of the top 10 players picked, selection between picks 11 and 50, or selected after pick 50), NFL winning ratio (percentage of games won), and QB production score (higher scores indicate more productive QBs). The researchers discovered that draft position is only weakly related to a quarterback鈥檚 performance in the NFL. They concluded that 鈥渜uarterbacks taken higher [in the draft] do not appear to perform any better.鈥
a. What is the experimental unit for this study?
b. Identify the type (quantitative or qualitative) of each variable measured.
c. Suppose you want to use this study to project the performance of future NFL QBs. Is this an application of descriptive or inferential statistics? Explain.
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