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Chapter 1: Q2. (page 49)
Explain the difference between descriptive and inferential statistics.
Descriptive statistics deals with different measures of the central tendency of sample data whereas inferential statistics deals with the usage of statistical tools to draw statistical conclusions.
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Random-digit dialing. To ascertain the effectiveness of their advertising campaigns, firms frequently conduct telephone interviews with consumers using random-digit dialing. With this approach, a random number generator mechanically creates the sample of phone numbers to be called. Each digit in the phone number is randomly selected from the possible digits 0, 1, 2, . . . , 9. Use the procedure to generate five seven-digit telephone numbers whose first three digits (area code) are 373.
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.
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.
Jamming attacks on wireless networks. Terrorists often use wireless networks to communicate. To disrupt these communications, the U.S. military uses jamming attacks on the wireless networks. The International Journal of Production Economics (Vol. 172, 2016) described a study of 80 such jamming attacks. The configuration of the wireless network attacked was determined in each case. Configuration consists of network type (WLAN, WSN, or AHN) and number of channels (single- or multi-channel).
a. Suppose the 80 jamming attacks represent all jamming attacks by the U.S. military over the past several years, and these attacks are the only attacks of interest to the researchers. Do the data associated with these 80 attacks represent a population or a sample? Explain.
b. The 80 jamming attacks actually represent a sample. Describe the population for which this sample is representative.
c. Identify the variable 鈥渘etwork type鈥� as quantitative or qualitative.
d. Identify the variable 鈥渘umber of channels鈥� as quantitative or qualitative.
e. Explain how to measure number of channels quantitatively?
Explain why would a statistician consider an inference incomplete without an accompanying measure of its reliability?
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