Mathematics / Statistics

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. 

#1   While there is a significant cost difference in the two sample sizes, there is also a significant difference in the accuracy of the data provided by the two samples. The sample size of 100, while about one fifth of the price of the 1000 home sample, is actually almost ten times less accurate. The margin of error for the smaller sample is $4,900.00, meaning that the true mean could be between $305,100.00 and $314.900.00, a $9,800.00 range. Conversely, the margin of error for the 1000 home sample is much smaller at $495.95, this is a much smaller range of $992, nearly one tenth of the range of the 100 home sample. I am 95% confident, using the 1000 home sample, that the true mean of houses in this area is between $309,504 and $310,496, which is a much more specific estimate than the 100 home sample can provide. In short, the 1000 home sample, while five times more expensive, will provide data to prepare the realtors that is ten times more accurate, which will ultimately improve their results and save money long term.  

#2  While looking at the options that the company has given you may seem like a lot. The one that cost more money gives your own company the ability to make more money with the information given. Yes, with the cost that you spend on the first option is way less, you also get less of a guaranty. You have a margin error of $25,000 which in my book is a lot more than I want to be gambling with. Plus, you are only looking at 100 listings instead of a 1,000 to put that into perspective even if 1% of those listings sold for the margin error of the $25,000, that is $250,000 out of your pocket just because you didn’t want to spend the initial startup fee.

As for the other option and again it is more but you are getting more out of it. You are getting more of a guaranty. The margin error is only $8,000 instead of $25,000 which is a whole lot less and lets just put out there if 1% of that 1000 was to be in the margin error you would only be out $80,000 and though that is still a lot of money it is still way less than the $250,000 in the other option.