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 $5,000
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
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