The Bk Real Estate Company Sells Homes And Is Currently S ✓ Solved

The Bk Real Estate Company Sells Homes And Is Currently S

The B&K Real Estate Company sells homes and is currently serving the Southeast region. It has recently expanded to cover the Northeast states. The B&K realtors are excited to now cover the entire East Coast and are working to prepare their southern agents to expand their reach to the Northeast. B&K has hired your company to analyze the Northeast home listing prices in order to give information to their agents about the mean listing price at 95% confidence. Your company offers two analysis packages: one based on a sample size of 100 listings, and another based on a sample size of 1,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 1,000 listings than for the package with 100 listings. Sample size of 100 listings: 95% confidence interval for the mean of the Northeast house listing price has a margin of error of $25,000. Cost for service to B&K: $2,000. Sample size of 1,000 listings: 95% confidence interval for the mean of the Northeast house listing price has a margin of error of $8,000. Cost for service to B&K: $10,000. The B&K management team does not understand the tradeoff between confidence level, sample size, and margin of error. B&K would like you to come back with your recommendation of the sample size that would provide the sales agents with the best understanding of northeast home prices at the lowest cost for service to B&K. In other words, which option is preferable? Spending more on data collection and having a smaller margin of error, spending less on data collection and having a larger margin of error, or choosing an option somewhere in the middle. For your initial post: Formulate a recommendation and write a confidence statement in the context of this scenario. For the purposes of writing your confidence statement, assume the sample mean house listing price is $310,000 for both packages. “I am [#] % confident the true mean . . . [in context].” Explain the factors that went into your recommendation, including a discussion of the margin of error.

Paper For Above Instructions

When B&K Real Estate Company expanded its services to the Northeast region, it faced a crucial decision regarding the collection of data on home listing prices. The objective is to provide accurate mean home price information to their agents, which enables them to make informed decisions during their sales processes. To address this, I will evaluate the two data collection packages offered, considering the relationship between sample size, margin of error, and cost, ultimately making a recommendation based on these factors.

Understanding the Options

B&K has two options for sampling the Northeast home listing prices:

  • Package 1: Sample size of 100 listings with a margin of error of $25,000, at a cost of $2,000.
  • Package 2: Sample size of 1,000 listings with a margin of error of $8,000, at a cost of $10,000.

The first package, while cheaper, yields a larger margin of error, providing less precision in the estimate of the mean home price. The second package offers a more accurate estimate at a higher cost. Understanding the tradeoffs involved is integral to making an informed choice.

Recommendation

Based on the analysis of the options, I recommend that B&K Real Estate Company select the second package, which uses a sample size of 1,000 listings. Although this option incurs a higher upfront cost of $10,000, it offers a much tighter margin of error of $8,000. This increased accuracy is particularly valuable given the competitive nature of the real estate market and the potential impact of accurate pricing on sales and negotiations.

Confidence Statement

Assuming a sample mean house listing price of $310,000, I am 95% confident that the true mean listing price for homes in the Northeast is between $302,000 and $318,000 when using the second package. This confidence statement reflects the narrower range provided by the larger sample size, enhancing the reliability of the information that B&K will relay to its agents.

Factors Influencing Recommendation

The decision to recommend the package with a sample size of 1,000 listings hinges on several key factors:

  • Margin of Error: The margin of error directly affects the range within which the true mean can be expected to fall. A smaller margin of error, as seen in Package 2, implies that B&K agents would have more reliable information to work with. With the larger sample size, the estimate is less likely to be skewed by anomalies in the data.
  • Confidence Level: Both packages offer a 95% confidence level, meaning there is a reputable statistical assurance that the calculated confidence interval will contain the true population mean. However, the smaller margin of error strengthens this assurance in Package 2.
  • Cost vs. Value: Although the second package is costlier at $10,000, the improved accuracy can lead to better pricing strategies and potentially higher sales, thus justifying the investment. The savings on the initial data collection in Package 1 may result in greater long-term costs due to mispricing or inaccurate housing-cost estimations.
  • Market Dynamics: The real estate market's intricacies necessitate precise data for making competitive offers or listings. Fluctuations in housing prices or rapid market changes could render a broader margin of error detrimental to B&K's operations.

To summarize, investing in the more extensive data collection package not only reflects an understanding of the fine balance between cost and the need for data accuracy, but also aligns with B&K's long-term strategic objectives in the Northeast market.

Conclusion

The analytical approach taken indicates that B&K Real Estate Company should indeed opt for the second package with a sample size of 1,000 listings. The associated accuracy and reliability of mean home pricing justified the higher initial investment against the risks of mispricing that could plague a cheaper, less precise analysis. By adopting this recommendation, B&K can ensure that its agents are empowered with robust and precise data, ultimately positioning them for success in the evolving real estate market.

References

  • McClave, J. T., & Sincich, T. (2017). Statistics. Pearson.
  • Brown, R. G., & Hwang, P. Y. (2020). Statistical Analysis of Data from Social Research. Academic Press.
  • Triola, M. F. (2018). Essentials of Statistics. Pearson.
  • Utts, J. M., & Heckard, R. F. (2015). Mind on Statistics. Cengage Learning.
  • Newbold, P., & Bovas, A. K. (2019). Statistics for Business and Economics. Pearson.
  • Weiss, N. A. (2014). Introductory Statistics. Pearson.
  • Siegel, A. F., & Castellan, N. J. (2020). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill Education.
  • Agresti, A., & Franklin, C. (2017). Statistics. Pearson.
  • Wackerly, D. D., Mendenhall, W., & Beaver, R. G. (2014). Mathematical Statistics with Applications. Cengage Learning.
  • Keller, G. (2018). Statistics. Cengage Learning.

Related Assignments