QUESTION
Discussion Replies
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 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 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.
| Subject | Statistics | Pages | 4 | Style | APA |
|---|
Answer
Using Confidence Level to Determine Sample Size and Margin of Error
The probability of expecting the probable samples to have a correct population constraint is the confidence level. The calculation is
CI = Sample mean ± Margin of error
Where sample mean = 310000
For 1000 sample size
CI = 310000 ± 8000
= (302000, 318000)
I am 95% confident that the true mean of the Northeast house listing cost is between 302000 dollars and 318000 dollars.
For 100 sample size
CI = 310000 ± 25000
= (285000, 335000)
I am 95% confident that the true mean of the Northeast house listing cost is between 285000 dollars and 335000 dollars.
In order to lower margin of error we have to increase the sample size. Increasing sample size will result in increasing data collection cost. Consequently, the correct sample size should be determined in a way that the margin of error is tolerable and the cost of collecting data low. Hence,the company should decide on the 100-sample size. This because it has a wide confidence interval and the cost of services is low.
The elements to consider in computing confidence intervals are margin of error and mean. The margin of error illustrates the proportion of the sample statistic that will vary from the actual population.
The representatives should opt for a broader confidence interval because it will provide them with broad options to pick from their listing price.
The benefit of a broad interval is that it will aid the representatives cater for the consumer requirements conferring to their financial plan. The disadvantage of a broad interval, the interval will not be accurate for the actual population.
For t
Discussion 2
he sample size of 1000, margin of error of 1000, and cost of 10000
CI = 310000 ± 1000
= (309000, 311000)
I am 95% confident that the true mean of the Northeast house listing cost is between 309000 dollars and 311000 dollars.
The initial option of using a sample size of 100 is preferable to this second option of confidence interval. The first option has a wide confidence interval and a lower service cost while this option, in as much as it has a low margin of error, the confidence interval is not wide, the cost of services is high, and the cost of data collection will be high as well.
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