6-3 Discussion: Confidence Intervals feedback

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.

I am attaching the 2 peer discussions that need a response separately. Please follow the above directions from the professor. I will upload also the example of the discussion.
I am supposed to turn it in by midnight tonight in the eastern timezone. Just need you to answer the questions the professor is asking to answer within the discussion my peer wrote.
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Peer # 1
6-3 Discussion: Confidence Intervals

B & K Real Estate,

For the Northeast region home listings prices with two packages:

Sample size of 100 listings:
95% confidence interval for the mean of the Northeast house, the 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
For the sample size of 100 listings, with the margin of error of $25,000 the listing prices would be between $285,000 and $335,000 for the cost of $2,000.
For the sample size of 1,000 listings, with the margin of error of $8000 the listing prices would be between $302,000 and $318,000 for the cost of $10,000. With the sample size of 1000 listings, you would have more listings for a smaller margin of error.

I am 95% confident that the true mean is between $302,000 and $318,000 with a smaller margin of error and would be a better value for 1000 listings than the lesser amount of 100 listings with a higher margin of error.

Detail Response:

Peer # 2
6-3 Discussion: Confidence Intervals: Shane Fonseca posted Feb 12, 2021 2:57 AM
The B&K team does not understand the tradeoff between the confidence level, sample size, and margin of error. It’s my understanding that the B&K team needs me to come up with a recommendation of a sample size to provide to the sales agents with the prices of the northeast homes at the lowest cost of services. That being said, the key in this instance for the B&K team, is to create a smaller margin of error and utilize more funds than to have an increase margin of error and spend less funds.
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
With these findings, the better route for the B&K team would be to go with the sample size of 1,000 with a smaller margin of error at $8,000. This would give the B&K team with roughly $17,000 in difference in margin of error. The B&K team would be able to make up the smaller margin of error fairly quickly without losing any profits or revenue.
Based on the sample mean being $310,000 and with a 100-sample size, the range of margin would be between $305,000 – $315,000. And, based on the sample size being 1000, the range of margin would be between $309,000 – $310,000.
That being said, I can come to a conclusion that I am 95% confident that the true mean would be between $309,000 – $310,000.

Detail response: