MAT 240 Week 6 Discussion | Southern New Hampshire University
- southern-new-hampshire-university / MAT 240
- 05 Jul 2022
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MAT 240 Week 6 Discussion | Southern New Hampshire University
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
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.
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