Reference no: EM132856945

Please explain these questions.

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 $8,000
• 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 writ e 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

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.

To the B&K Real Estate Company:

I am pleased to be have this opportunity to work with you and I am 95% confident the true mean of the Northeast house listing prices falls between $302,000 and $318,000. The 95% represents the probability that the true mean is contained in a confidence interval if the estimator is used repeatedly.

I am here to shed a little light on our available data collection packages and what they entail. So first off, our first package includes a sample size of 100 listings with a confidence level of 95% and a margin of error of $25,000. Our second package includes a sample size of 1,000 listings with a confidence level of 95% and a margin of error of only $8,000. The two packages do have a price difference which is based on the amount of data collected. Option one costs only $2,000 while option two cost $10,000. Now for the breakdown of what these statements mean and what you would be paying for.

In my opinion, option two is the best option to go with. Why do you ask? Well let's break it down. First, the sample size is larger. A larger sample size means a more accurate margin of error meaning that the data is more precise and less likely to falter. Next, the confidence level is a 95% confidence interval for both of the options, however, what this means is that the 5% error is much smaller in option two due to the larger sample size, so instead of a $25,000 margin of error like in option one, option two gives only a margin of error of $8,000. So what this means is there could be a +/- of $8,000 to the $310,000 [$302,000, $318,000] sample mean house listing price. That is a great margin to work with when speaking in the sense of home listing prices. So even though you may be spending a little more for the data collection it gives you a much smaller margin to work with in turn creating a tighter variance to work with. And in my opinion, when working with money, the more precise you are the better, right?