What advantages and disadvantages would there be in having different confidence intervals for the agents?

Learning Goal: I’m working on a applied mathematics discussion question and need an explanation and answer to help me learn.6-1 Discussion: Confidence IntervalsThe
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.