The BK Real Estate Company Sells Homes And Is Currently Serv ✓ Solved
The Bk Real Estate Company Sells Homes And Is Currently Servi
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 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. 95% confidence interval for the mean of the Northeast house listing price has a margin of error of $25,000 for the sample size of 100 listings, costing $2,000. For the sample size of 1,000 listings, the margin of error is $8,000 and the cost is $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?
For your initial post: Formulate a recommendation and write a confidence statement in the context of this scenario. 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
The B&K Real Estate Company has a crucial decision to make regarding the analysis of home listing prices in the Northeast. The two available packages to consider are based on sample sizes of 100 and 1,000 listings with corresponding margins of error of $25,000 and $8,000, respectively. In this essay, a recommendation will be made, based on an analysis of the benefits and costs of each package while considering the implications of confidence intervals and marginal errors.
Understanding Sample Sizes and Margins of Error
The concept of sample size is integral to statistical analysis, especially in estimating population parameters. The sample size directly influences the accuracy of the estimates. A larger sample size typically provides a smaller margin of error, enhancing the reliability of the confidence intervals. For B&K, the mean house listing price in the Northeast has been estimated at $310,000.
The sample size of 100 listings provides a margin of error of $25,000, leading to a confidence interval of $285,000 to $335,000. In contrast, the larger sample size of 1,000 listings results in a margin of error of $8,000, producing a more precise confidence interval of $302,000 to $318,000. This distinction highlights that while both analyses will provide valuable insights, the latter offers a more precise estimate of the true mean listing price.
Cost-Benefit Analysis
While the precision of the larger sample is appealing, the cost associated with obtaining that data is a key factor in the decision-making process. The package based on 100 listings costs $2,000, while the larger sample of 1,000 listings incurs a cost of $10,000. Upon evaluating these costs, the B&K management must weigh their budget against the need for accuracy in understanding the market. Aiming for a balance between cost-effectiveness and the quality of information is imperative.
Recommendation
In light of the analysis, I recommend that B&K should opt for the package with a sample size of 1,000 listings. By choosing this option, the company can achieve a margin of error of $8,000, leading to a more precise understanding of the Northeast home prices. The additional investment of $10,000 is justifiable, considering the critical nature of their market expansion efforts. Investing in accurate data is essential, as the costs associated with poor decision-making based on incomplete or less reliable information could far exceed the initial investment.
Therefore, the confidence statement derived from this decision is: “I am 95% confident that the true mean listing price of homes in the Northeast is between $302,000 and $318,000.” This statement emphasizes the precision of the larger sample size and provides the sales agents with a more exact analysis of the market that they will be entering.
Factors Influencing the Recommendation
The recommendation is influenced primarily by three factors: the margin of error, the cost of data collection, and the strategic importance of accurate information. A smaller margin of error enhances decision-making by providing a clearer picture of pricing trends and enabling the sales agents to set competitive prices effectively. The cost of obtaining the data must be retained in check to ensure that the investment aligns with the potential benefits gained from accurate insights. Finally, the strategic importance of operating in a new market segment warrants a more thorough understanding of pricing to mitigate risks associated with insufficient information.
Conclusion
In the competitive landscape of real estate, data-driven decisions are paramount. The ability to accurately gauge market conditions in the Northeast will provide B&K's sales agents with the tools necessary to successfully navigate their expansion. By selecting the package with a sample size of 1,000 listings, B&K is poised to make informed decisions grounded in precise data. The analysis supports the notion that greater accuracy justifies the additional cost, allowing the company to foster trust and success as it enters this new market.
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