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 though process and reasoning in your response. This is my peer response post. In my opinion, the preferable option is choosing the option that is somewhere in the middle. The larger our sample size, the smaller the margin of error. However, we do not want to use the most expensive option to reduce costs. Therefore, we should use the middle option. If the sample mean house listing is $310,000 and we would use the silver package, my confidence statement would be:
“I am 95% confident that the true mean of a house listing price in the Northeast is between the lower ($302,250) and upper ($317,750) bound.”
In order to find the lower bound, we deduct $7,750 from the sample mean of $310,000 (310,000-7,750=302,250), and in order to find the upper bound, we add $7,750 to the sample mean (310,000+7,750=31 7,750. Below is my Initial post.Recommendation to the B&K Real Estate Company
In light of the information that has been presented, my advice to the B&K Real Estate Company would be to go with the Silver Package, which includes a listing sample size of one thousand properties. When predicting the median listing price in the Northeastern region, this approach achieves a good compromise between the amount of money spent and the level of accuracy achieved.
The margin of error for the confidence interval for the mean of the Northeast house listing price in the Silver Package is $7,750. The confidence interval is calculated using the data from the Silver Package. We are able to determine the confidence interval using the following formula, assuming that the sample mean house listing price for all packages is $310,000: $310,000 $7,750. This indicates that we have a confidence level of 95% that the actual mean listing price lies somewhere within this range.
The following are some of the statistical considerations that led to this recommendation concerning the three choices available to the company:
The cost of the Silver Package is lower than the cost of the Gold Package, making the Silver Package a more cost-effective option for B&K Real Estate Company. They will be able to acquire an acceptable level of precision in their estimation of the mean listing price if they go with the Silver Package. This will allow them to keep their costs within reasonable limits.
The term “margin of error” refers to the potential range of values that the “true mean listing price” could end up falling inside (Anderson et al 2019). The error range for the Silver Package is between $7,500 and $8,250. Despite the fact that this error margin is greater than the one included in the Gold Package, the B&K realtors are still provided with a sufficient level of precision to enable them to make educated choices. A higher margin of error gives rise to a wider spread of potential mean values, but it does so at the expense of a lower cost overall.
When all of these factors are taken into account, the B&K Real Estate Company finds that the Silver Package offers the optimal combination of low cost and high precision. At a cost of $10,000, it offers sales representatives in the Northeast a comprehensive overview of the region’s housing market conditions.
declaration of confidence: “I am 95% confident that the true mean listing price for homes in the Northeast falls within the range of $302,250 to $317,750 based on the analysis of 1,000 listings provided in the Silver Package.” This declaration is based on the fact that the Silver Package includes 1,000 listings.
Reference
Anderson, A. A. (2019). Assessing statistical results: magnitude, precision, and model uncertainty. The American Statistician, 73(sup1), 118-1
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