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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List and define the four elements of a descriptive statistics problem.
The “lucky store effect” in lottery ticket sales. In the American Economic Review (Vol. 98, 2008), University of Chicago researchers investigated the lucky store effect theory in lottery ticket sales, i.e., the theory that a lottery retail store that sold a large-prize-winning ticket will experience greater ticket sales the following week. The researchers examined the weekly ticket sales of all 24,400 active lottery retailers in Texas. The analysis showed that “the week following the sale of [a winning Lotto Texas ticket], the winning store experiences a 12 to 38 percent relative sales increase. . . . ” Consequently, the researchers project that future winning lottery retail stores will experience the lucky store effect. Is this study an example of descriptive statistics or inferential statistics? Explain.
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)
Zillow.com estimates of home values. Zillow.com is a real estate Web site that provides free estimates of the market value of homes. A trio of University of Texas at San Antonio professors compared Zillow estimates to actual sale prices of homes and published their results in The Appraisal Journal (Winter 2010). The analysis was based on data collected for 2,045 single-family residential properties in Arlington, Texas, that sold during the last 6 months of 2006. Sale price and Zillow estimated value (in dollars) were measured for each property. Zillow claims that this market has one of its highest-accuracy ratings. However, the research revealed that Zillow overestimated the market value by more than 10% for nearly half of the properties.
a. What is the experimental unit for this study?
b. Describe the variables measured in the study. Do these variables produce quantitative or qualitative data?
c. Give a scenario where the 2,045 properties represent a population.
d. If the 2,045 properties represent a representative sample from a population, describe the population.
e. Suppose the relevant population is all single-family residential properties in the United States. Do you believe the 2,045 properties are representative of this population? Explain.
List and define the five elements of an inferential statistical analysis.
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