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. Undergraduate Discussion Rubric Overview Your active participation in the discussions is essential to your overall success this term. Discussion questions will help you make meaningful connections between the course content and the larger concepts of the course. These discussions give you a chance to express your own thoughts, ask questions, and gain insight from your peers and instructor. Directions For each discussion, you must create one initial post and follow up with at least two response posts. For your initial post, do the following: Write a post of 1 to 2 paragraphs. In Module One, complete your initial post by Thursday at 11:59 p.m. Eastern. In Modules Two through Eight, complete your initial post by Thursday at 11:59 p.m. of your local time zone. Consider content from other parts of the course where appropriate. Use proper citation methods for your discipline when referencing scholarly or popular sources. For your response posts, do the following: Reply to at least two classmates outside of your own initial post thread. In Module One, complete your two response posts by Sunday at 11:59 p.m. Eastern. In Modules Two through Eight, complete your two response posts by Sunday at 11:59 p.m. of your local time zone. Demonstrate more depth and thought than saying things like “I agree” or “You are wrong.” Guidance is provided for you in the discussion prompt. Discussion Rubric Criteria Exemplary Proficient Needs Improvement Not Evident Value Comprehension Develops an initial post with an organized, clear point of view or idea using rich and significant detail (100%) Develops an initial post with a point of view or idea using adequate organization and detail (85%) Develops an initial post with a point of view or idea but with some gaps in organization and detail (55%) Does not develop an initial post with an organized point of view or idea (0%) 40 Timeliness N/A Submits initial post on time (100%) Submits initial post one day late (55%) Submits initial post two or more days late (0%) 10 Engagement Provides relevant and meaningful response posts with clarifying explanation and detail (100%) Provides relevant response posts with some explanation and detail (85%) Provides somewhat relevant response posts with some explanation and detail (55%) Provides response posts that are generic with little explanation or detail (0%) 30 Writing (Mechanics) Writes posts that are easily understood, clear, and concise using proper citation methods where applicable with no errors in citations (100%) Writes posts that are easily understood using proper citation methods where applicable with few errors in citations (85%) Writes posts that are understandable using proper citation methods where applicable with a number of errors in