Solved: Zillow.com estimates of home values. Zillow.com is

Chapter 6, Problem 45E

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QUESTION:

Problem 45e

Zillow.com estimates of home values. Zillow.com is a real estate Web site that provides free estimates of the market value of homes. Refer to The Appraisal Journal (Winter 2010) study of the accuracy of Zillow’s estimates, Exercise 1.15 (p. 25). Data were collected for a sample of 2,045 single-family residential properties in Arlington, Texas. The researchers determined that Zillow overestimated by more than 10% the market value of 818 of the 2,045 homes. Suppose you want to estimate p, the true proportion of Arlington, Texas, homes with market values that are overestimated by more than 10% by Zillow.

a. Find , the point estimate of p.

b. Describe the sampling distribution of .

c. Find a 95% confidence interval for p.

d. Give a practical interpretation of the confidence interval, part c.

e. Suppose a Zillow representative claims that p = .3. Is the claim believable? Explain.

Questions & Answers

QUESTION:

Problem 45e

a. Find , the point estimate of p.

b. Describe the sampling distribution of .

c. Find a 95% confidence interval for p.

d. Give a practical interpretation of the confidence interval, part c.

e. Suppose a Zillow representative claims that p = .3. Is the claim believable? Explain.

ANSWER:

Step 1 of 7

(a)

Compute, the point estimate of p.

Let the sample size be 2,045 and number of success be 818.

The mean of the sampling distribution of the sample proportion is the population proportion. The sample proportion is an unbiased estimator of the population proportion (p).