Parking at a university. Parking at a large university has become a big problem. The university's administrators want to determine the average parking time of its students. An administrator inconspicuously followed 250 students and carefully recorded the time it took them to find a parking spot.
a. What is the population of interest to the university administration?
b. Identify the sample of interest to the university administration.
c. What is the experimental unit of interest to the university administration?
d. What is the variable of interest to the university administration?
a. The entire group of students that park their vehicles at the university.
b. 250 students who park their vehicles at the university for whom the time is noted.
c. 250 students for which the data was amassed.
d. The time taken by the students to find a parking spot.
The population of interest can be seen as the group with items of similar attributes, and by using analysis, the conclusion is drawn. Here, the population of interest for the administration is the batch of individuals who park at their university.
The sample of interest denotes the subset of the population that the researcher wants to study. In this case, the sample of interest is the 250 students who park their vehicles at the university. For them, the time is noted.
The experimental unit is the primary unit, which the statistician wants to analyze, study about, and hence make conclusions. This is the main subject of the research study. Hence, in this case, it is 250 students on whom the study is being conducted.
Variable of interest indicates the factor that does not remain stagnant and can be altered. In this scenario, the variable is the time taken by individuals to locate the parking spot.
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’s performance in the NFL. They concluded that “quarterbacks taken higher [in the draft] do not appear to perform any better.”
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.
Monitoring the production of soft-drink cans. The Wakefield plant of Coca-Cola and Schweppes Beverages Limited (CCSB) can produce 4,000 cans of soft drink per minute. The automated process consists of measuring and dispensing the raw ingredients into storage vessels to create the syrup and then injecting the syrup, along with carbon dioxide, into the beverage cans. In order to monitor the sub process that adds carbon dioxide to the cans, five filled cans are pulled off the line every 15 minutes, and the amount of carbon dioxide in each of these five cans is measured to determine whether the amounts are within prescribed limits.
a. Describe the process studied.
b. Describe the variable of interest.
c. Describe the sample.
d. Describe the inference of interest.
e. Brix is a unit for measuring sugar concentration. If a technician is assigned the task of estimating the average brix level of all 240,000 cans of beverage stored in a warehouse near Wakefield, will the technician be examining a process or a population? Explain.
The economic return to earning an MBA. What are the economic rewards (e.g., higher salary) to obtaining an MBA degree? This was the question of interest in an article published in the International Economic Review (August 2008). The researchers made inferences based on wage data collected for a sample of 3,244 individuals who sat for the Graduate Management Admissions Test (GMAT). (The GMAT exam is required for entrance into most MBA programs.) The following sampling scheme was employed. All those who took the GMAT exam in any of four selected time periods were mailed a questionnaire. Those who responded to the questionnaire were then sent three follow-up surveys (one survey every 3 months). The final sample of 3,244 represents only those individuals who responded to all four surveys. (For example, about 5,600 took the GMAT in one time period; of these, only about 800 responded to all four surveys.)
A. For this study, describe the population of interest.
b. What method was used to collect the sample data?
c. Do you think the final sample is representative of the population? Why or why not? Comment on potential biases in the sample.
Current population survey. The employment status (employed or unemployed) of each individual in the U.S. workforce is a set of data that is of interest to economists, businesspeople, and sociologists. To obtain information about the employment status of the workforce, the U.S. Bureau of the Census conducts what is known as the Current Population Survey. Each month interviewers visit about 50,000 of the 117 million households in the United States and question the occupants over 14 years of age about their employment status. Their responses enable the Bureau of the Census to estimate the percentage of people in the labor force who are unemployed (the unemployment rate).
a. Define the population of interest to the Census Bureau.
b. What variable is being measured? Is it quantitative or qualitative?
c. Is the problem of interest to the Census Bureau descriptive or inferential?
d. In order to monitor the rate of unemployment, it is essential to have a definition of unemployed. Different economists and even different countries define it in various ways. Develop your own definition of an "unemployed person." Your definition should answer such questions as: Are students on summer vacation unemployed? Are college professors who do not teach summer school unemployed? At what age are people considered to be eligible for the workforce? Are people who are out of work but not actively seeking a job unemployed?
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