I’m working on a applied mathematics discussion question and need an explanation and answer to help me learn.

6-1 Discussion: Confidence Intervals

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.