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 three analysis packages: one based on a sample size of 100 listings, one based on 1,000 listings, and another based on a sample size of 4,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 4,000 listings than for the package with 100 listings.
Bronze Package – Sample size of 100 listings:
95% confidence interval for the mean of the Northeast house listing price has a margin of error of $24,500
Cost for service to B&K: $2,000
Silver Package – Sample size of 1,000 listings:
95% confidence interval for the mean of the Northeast house listing price has a margin of error of $7,750
Cost for service to B&K: $10,000
Gold Package – Sample size of 4,000 listings:
95% confidence interval for the mean of the Northeast house listing price has a margin of error of $3,900
Cost for service to B&K: $25,000
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 all 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
For your response posts to your peers, choose two different confidence intervals for your responses. Do you think the agents would prefer a different confidence interval than their management? What advantages and disadvantages would there be in having different confidence intervals for the agents? Explain your thought process and reasoning in your response.
post 1
I am 95% confident the true mean house listing for the Northeast is between $285,500 and $334,500 with a margin error of $7,750. Utilizing the Silver package with the sample size of 1,000 listings out of the Northeast population. This margin of error of $7,750 is typically preferable to invest more in the data collection to reduce the margin of error. This ensures that your conclusions are based on reliable and precise information.
post2
I would recommend the Silver Package with a sample size of 1,000 listings for B&K. My confidence statement would be “I am 95% confident the true mean listing price of Northeast homes falls within the range of $302,250 to $317,750.” This option strikes a balance between cost and precision. While the Bronze Package is cheaper it has a larger margin of error might compromise the accuracy needed for informed decisions. On the other hand the Gold Package offers the smallest margin of error but at a significantly higher cost. As the sample size increases, the margin of error decreases. The Silver Package’s margin of error $7,750 is acceptable for B&K’s purposes, providing a reasonably narrow range around the estimated mean listing price and ensuring agents have a fairly accurate understanding of the market. A 95% confidence level is standard and offers a good balance between confidence and precision. It indicates a 95% chance that the true mean listing price falls within the calculated interval, giving B&K reasonable assurance in their decision-making process.
