Sampling Distributions – Real Estate Part 2

Sampling Distributions – Real Estate Part 2

Directions: Use the real estate data you used for your Week 2 learning team assignment. Analyze the data and explain your answers.
1. Review the data and for the purpose of this project please consider the 100 listing prices as a population.
• Explain what your computed population mean and population standard deviation were.

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Population mean was determined to be $193,262.86
Population standard deviation was determined to be $97382.96
2. Divide the 100 listing prices into 10 samples of n=10 each. Each of your 10 samples will tend to be random if the first sample includes houses 1 through 10 on your spreadsheet, the second sample consists of houses 11 through 20, and so on.
• Compute the mean of each of the 10 samples and list them:

$ 255,460.00
$ 211,380.00
$ 213,820.00
$ 188,750.00
$ 146,840.00
$ 196,360.00
$ 196,340.00
$ 178,330.00
$ 167,870.00
$ 184,950.00

3. Compute the mean of those 10 means.
• Explain how the mean of the means is equal, or not, to the population mean of the 100 listing prices from above.

The mean of the 10 means is $194010.00

Although the mean of the samples does not equal the mean of the whole data, it is only $747.14 off. Since much of the data collected for statistical purposes is from a sample, we can assume that the mean collected from the samples is fairly accurate for the population. The reason we see a difference here could be sampling error. With any sample, there is always the possibility that the sample yields different results than the information the entire population would provide.
4. Compute the standard deviation of those 10 means and compare the standard deviation of the 10 means to the population standard deviation of all 100 listing prices.
• Explain why it is significantly higher, or lower, than the population standard deviation.

5. Explain how much more or less the standard deviation of sample means was than the population standard deviation. According to the formula for standard deviation of sample means, it should be far less. (That formula is σ = σ/√n = σ/√10 = σ/3.16 ) Does your computed σ agree with the formula?
6. According to the Empirical Rule, what percentage of your sample means should be within 1 standard deviation of the population mean? Using your computed σ, do your sample means seem to conform to the rule?
7. According to the Empirical Rule, what percentage of your sample means should be within 2 standard deviations of the population mean? Again, do your sample means seem to conform to the rule?

You used the Empirical Rule because it really gives us more information (and because I asked you to), but truthfully you should have used Chebyshev’s Theorem. Even though Chebyshev’s doesn’t tell us much, why should you ha

Sampling Distributions – Real Estate Part 2

Sampling Distributions – Real Estate Part 2