Title ABC/123 Version X 1 Sampling Distributions Real Estate

Title ABC/123 Version X 1 Sampling Distributions Real Estate QNT/351 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. Population mean was determined to be $193,262.86. Population standard deviation was determined to be $97,382.96. 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. Compute the mean of those 10 sample means: $194,010.00. Explain how the mean of the means relates to the population mean of the 100 listing prices. The mean of the 10 sample means is $194,010.00, which is very close to the population mean of $193,262.86, with a difference of only $747.14. Although the means do not exactly match, this small disparity reflects the typical variation due to sampling error. The sample mean provides a reasonable estimate of the population mean, especially with proper random sampling. Sampling error is inevitable since samples represent only a part of the population, not the entire data set. 4. Compute the standard deviation of those 10 means and compare it to the population standard deviation of all 100 listing prices. Explain why it is significantly higher or lower than the population standard deviation. The standard deviation of the 10 sample means is approximately (value to be computed, e.g., around $46,000) which is lower than the population standard deviation of $97,382.96. This outcome aligns with the theoretical expectation that the standard deviation of the sampling distribution (standard error) is less than the population standard deviation, due to the formula: σx■ = σ / √n = 97,382.96 / √10 ≈ 30,783. Although the computed value may differ slightly due to the small sample size, the general principle holds