Business Studies

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
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

ANSWER

The trade-off between confidence level, sample size, and margin of error is crucial for most if not all business decisions. For B&K Real Estate Company, the factors to consider are two, one is a sample size of a 100 listings with a 95% confidence level, a margin of error of $25,000 and a cost of service of $2000 and the other option is a sample size of 1000 listings with a confidence level of 95%, a margin error of $8000 and a cost service of $10,000. From these factors, I am 95% confident that the true mean is $310,000 for both packages, however, spending more on data collection and having a smaller margin of error has more merits in comparison to spending less on data collection and having a larger margin of error.

The reason and logic for this recommendation are that while the service cost is once for the entire project, a margin of error could very well mean more losses in revenue for B&K. The difference between the margin of errors for both alternatives is $17,000 which is more than the cost service for more data collection which is $10,000. By spending $8000 more on the service the company has a smaller margin of error to last the lifetime of the entire project. Practically, the margin of error for a unit on the first option could result in the sale of a unit at $285,000 while the same unit could go for $302,000 with the second option. This, however, is not conclusive because if there is a positive margin of error the cost of the unit would be $335,000 and $318,000 respectively. However, the goal is not to make incredible profits or losses but to maintain sustainable revenue meaning option two is still most viable.