Need help, answer to 2 peers:

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

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.

Peer 1- Hi class,

I am 95% confident that the true mean is in the confidence interval [$306,100, $313,900] and only 5% unsure if it is not. It’s a $25,000 cost to ensure that the margin of error is as small as possible (do to the large sample size of 4,000). The full range of the margin of error for the Gold Package is $7,800 compared to$49,000 (the Bronze Package) and $15,500 (the Silver Package). The more money spent the larger the sample can be and the more accurate the data will be.

Gold Package – Sample size of 4,000   listings:

Cost =

$25,000

CI (95%) =

1.96

Mean =

$310,000

m =

$3,900

L. bounds=

$306,100

U. bounds =

$313,900

Peer 2-

Hello Class,

Our company chose the Silver package.

Margin of error $7,750 Cost of service $10,000Confidence level $302,250-$317,750

I am 95% confident that the actual mean house listing price falls between $302,250-$317,750. We used the Silver package to determine the margin error is between both the bronze and silver package, and because the margin of error was only $7,750, they would still be able to get close enough to the actual value of the listing price. Having a lower cost of 10,000, they would only need to process the data once and come up with a better solution if necessary in the future, which would save them money in the long run. Sampling 1,000 homes can bring you closer to the true value of the listing price in the area.