Question

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.

Short answer

a. Each of the 2,045 single-family residential properties.

b. The market value and Zillow estimates are quantitative.

c. Data collected from each of 2,045 families owning each property.

d. All the single-family residential properties together can be referred to as the population.

e. Yes

Step-by-step solution

Defining the Experimental unit

In this context, the experimental unit is each property owned by each family in Texas. The market value of each of these properties has been taken into consideration for conducting research by the professors of the University of Texas.

Explaining the variables to be quantitative

The market value of the properties and the estimates of Zillow are numerical, and these variables are quantitative. Moreover, the University of Texas professors have conducted mathematical tests to draw numerical conclusions that can be possible with quantitative data.

Simplifying the scenario

In this case, let’s consider that all 2,045 families can collect the data from their respective properties.The total data collected will be equivalent to the total population living in that particular town.

Justifying the answer 

Texas is a part of the United States, and there are innumerable single-family properties.If only 2,045 of them are considered a sample, then all the single-family properties can be treated as the total population.

Reasoning for being in favor of the motion of the statement 

If all the single-family properties are treated as a representation of the population, then any number of properties must be treated as population. Therefore, 2,045 single-family properties will indicate the properties of the population.