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Chapter 1: Q7E (page 12)

A certain city divides naturally into ten district neighborhoods.How might a real estate appraiser select a sample of single-family homes that could be used as a basis for developing an equation to predict appraised value from characteristics such as age, size, number of bathrooms, distance to the nearest school, and so on? Is the study enumerative or analytic?

Short Answer

Expert verified

Simple random sampling and stratified random sampling can be used as a basis for developing an equation to predict appraised value from different characteristics.

The study is enumerative.

Step by step solution

01

Given information

The district neighbourhoods of a certain city are divided into ten.

02

Describe how a sample of single-family homes could be selected

The sampling procedures that can be used are:

1. Simple Random sampling:Simple random sampling can be used to select the sample of all single-family homes in the city. With this method, biasedness will be eliminated.

2. Stratified Random Sampling:With this method, a simple random sample from each of 10 district neighborhoods can be drawn and from each of the selected homes, the values of the desired variables can be determined.

03

Check whether the study is enumerative or analytic

An enumerative study is a study where the population is finite whereas an analytic study is a study where the population from which a sample is drawn is nonidentifiable.

The provided study is an enumerative study because the population from which the sample needs to be selected is finite and identifiable.

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Most popular questions from this chapter

The National Health and Nutrition Examination Survey (NHANES) collects demographic, socioeconomic, dietary, and health related information on an annual basis. Here is a sample of \({\rm{20}}\) observations on HDL cholesterol level \({\rm{(mg/dl)}}\) obtained from the \({\rm{2009 - 2010}}\) survey (HDL is 鈥済ood鈥� cholesterol; the higher its value, the lower the risk for heart disease):

\(\begin{array}{l}{\rm{35 49 52 54 65 51 51}}\\{\rm{47 86 36 46 33 39 45}}\\{\rm{39 63 95 35 30 48}}\end{array}\)

a. Calculate a point estimate of the population mean HDL cholesterol level.

b. Making no assumptions about the shape of the population distribution, calculate a point estimate of the value that separates the largest \({\rm{50\% }}\) of HDL levels from the smallest \({\rm{50\% }}\).

c. Calculate a point estimate of the population standard deviation.

d. An HDL level of at least \({\rm{60}}\) is considered desirable as it corresponds to a significantly lower risk of heart disease. Making no assumptions about the shape of the population distribution, estimate the proportion \({\rm{p}}\) of the population having an HDL level of at least \({\rm{60}}\).

The accompanying summary data on CeO2 particlesizes (nm) under certain experimental conditions wasread from a graph in the article 鈥淣anoceria鈥擡nergetics of Surfaces, Interfaces and WaterAdsorption鈥� (J. of the Amer. Ceramic Soc., 2011:3992鈥�3999):

3.0鈭�<3.5 3.5鈭�<4.0 4.0鈭�<4.5 4.5鈭�<5.0 5.0鈭�<5.5

5 15 27 34 22

5.5鈭�<6.0 6.0鈭�<6.5 6.5鈭�<7.0 7.0鈭�<7.5 7.5鈭�<8.0

14 7 2 4 1

a. What proportion of the observations are less than 5?

b. What proportion of the observations are at least 6?

c. Construct a histogram with relative frequency on the vertical axis and comment on interesting features. In particular, does the distribution of particle sizes appear to be reasonably symmetric or somewhat skewed? (Note:The investigators fit lognormaldistribution to the data; this is discussed in Chapter 4.)

d. Construct a histogram with density on the vertical axis and compare to the histogram in (c).

The May 1, 2009, issue of the Mont clarian reported the following home sale amounts for a sample of homes in Alameda, CA that were sold the previous month (1000s of $):

590 815 575 608 350 1285 408 540 555 679

  1. Calculate and interpret the sample mean and median.
  2. Suppose the 6th observation had been 985 rather than 1285. How would the mean and median change?
  3. Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations.
  4. Calculate a 15% trimmed mean.

The cdf for \({\rm{X( = measurement error)}}\) of Exercise \({\rm{3}}\) is

\({\rm{F(x) = }}\left\{ {\begin{array}{*{20}{c}}{\rm{0}}&{{\rm{x < - 2}}}\\{\frac{{\rm{1}}}{{\rm{2}}}{\rm{ + }}\frac{{\rm{3}}}{{{\rm{32}}}}\left( {{\rm{4x - }}\frac{{{{\rm{x}}^{\rm{3}}}}}{{\rm{3}}}} \right)}&{{\rm{ - 2}} \le {\rm{x < 2}}}\\{\rm{1}}&{{\rm{2}} \le {\rm{x}}}\end{array}} \right.\)

a. Compute \({\rm{P(X < 0)}}\).

b. Compute \({\rm{P( - 1 < X < 1)}}\).

c. Compute \({\rm{P(}}{\rm{.5 < X)}}\).

d. Verify that \({\rm{f(x)}}\) is as given in Exercise \({\rm{3}}\) by obtaining \({\rm{F'(x)}}\).

e. Verify that \(\widetilde {\rm{\mu }}{\rm{ = 0}}\).

Consider a sample \({x_1},{x_2},...,{x_n}\) with neven. Let \({\bar x_L}\) and \({\bar x_U}\) denote the average of the smallest n/2 and the largest n/2 observations, respectively. Show that the mean absolute deviation from the median for this sample satisfies

\(\sum {\left| {{x_i} - \tilde x} \right|} /n = \left( {{{\bar x}_U} - {{\bar x}_L}} \right)/2\)

Then show that if n is odd and the two averages are calculated after excluding the median from each half, replacing non the left with n-1 gives the correct result.(Hint: Break the sum into two parts, the first involving observations less than or equal to the median and the second involving observations greater than or equal to the median.)
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