Formulate a recommendation and write a confidence statement in the context of this scenario.

The B&Okay Actual Property Firm presently serves the Southeast space by promoting homes. It has recently prolonged to incorporate states within the Northeast. The B&Okay actual property brokers are delighted to cowl the entire East Coast and are getting ready their southern brokers to extend their presence within the Northeast. B&Okay has engaged your group to look at Northeast property itemizing costs with the intention to present its brokers with 95% confidence within the imply itemizing worth. Your group offers three evaluation packages, one primarily based on 100 listings, one primarily based on 1,000 listings, and one primarily based on 4,000 listings. Your agency fees extra for the package deal with 4,000 listings than for the package deal with 100 listings because of the expense of knowledge gathering.
Requirement
B&Okay requests that you just give a pattern dimension suggestion that may present gross sales representatives with essentially the most correct data of property pricing within the northeast on the lowest expense to B&Okay.
Calculations
To be able to present an applicable suggestion, the arrogance intervals for these packages shall be computed. The computations are as acknowledged within the desk under.
Bronze Bundle – 100 itemizing pattern dimension:
Imply of samples = $310,000
Error margin at 95% confidence interval is $24,500
Price for service rendered to B&Okay: $2000
The 95% confidence interval will seem like this: CI=pattern imply error margin
CI=310,000±24,500 sCI=(285500,334500)
Bundle Silver – Pattern dimension of 1 thousand listings:
Imply of samples = $310,000
95% confidence interval error margin is $7,750
$10,000 price for service rendered to B&Okay
The 95% confidence interval will seem like this: CI=pattern imply error margin
CI=310,000±7,750 sCI=(302250,317750)
Gold Bundle – Pattern of 4 thousand listings:
Imply of samples = $310,000
$3,900 95% confidence interval margin of error
$5,000 for service rendered to B&Okay
The 95% confidence interval will seem like this: CI=pattern imply error margin
CI=310,000±3,900 sCI=(306100,313900)
In quantitative analysis tasks, it’s stated that confidence intervals which can be narrower are often preferable. The target of any evaluation using confidence intervals is to all the time cut back the arrogance intervals within the sake of precision and accuracy. The diploma of confidence and pattern dimension are essentially the most influential variables on the decided confidence interval dimension. When the pattern dimension is huge, the arrogance intervals shall be extra exact.

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