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Chapter 1: Q1. (page 49)
What is statistics?
Statistics is a field of study where the theories of mathematics can be applied with the help of data collected by researchers.
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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.
Customer orders at a department store. A department store receives customer orders through its call center and website. These orders, as well as any special orders received in the stores are forwarded to a distribution center where workers pull the items on the orders from inventory, pack them, and prepare the necessary paperwork for the shipping company that will pick up the packages and deliver them to the customers. In order to monitor the subprocess of pulling the items from inventory, one order is checked every 15 minutes to determine whether the worker has pulled the correct item.
a. Identify the process of interest.
b. Identify the variable of interest. Is it quantitative or qualitative?
c. Describe the sample.
d. Describe the inference of interest.
e. How likely is the sample to be representative?
Inspection of highway bridges. All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration (FHWA). Data from the FHWA inspections are compiled into the National Bridge Inventory (NBI). Several of the nearly 100 variables maintained by the NBI are listed below. Classify each variable as quantitative or qualitative.
a. Length of maximum span (feet)
b. Number of vehicle lanes
c. Toll bridge (yes or no)
d. Average daily traffic
e. Condition of deck (good, fair, or poor)
f. Bypass or detour length (miles)
g. Route type (interstate, U.S., state, county, or city)
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 “network type” as quantitative or qualitative.
d. Identify the variable “number of channels” as quantitative or qualitative.
e. Explain how to measure number of channels quantitatively?
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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