The width of a confidence interval is directly proportional to the level of confidence. This means the width of the confidence interval increases when the level of confidence is increased. Another important factor is that the width of the confidence interval is inversely proportional to the sample size. This means that the width of the interval reduces when a larger sample size is taken. Basically, the confidence interval is directly impacted by the margin of error. When the confidence level is increased by keeping the sample size fixed the margin of error also increases. If the sample size is increased by keeping the confidence level fixed, the margin of error reduces [1]. The narrower the width of the interval, the greater the accuracy of the estimation. It would be best for the B&K Real Estate Company to spend more money on data collection and get a narrower confidence interval for the mean listing price of houses in the Northeast region. Hence, the suitable recommendation for the B&K Real Estate Company is to get the Gold Package. The cost for the Golf Package is $25,000. In this package, the listing price of 4000 houses are gathered to compute the 95% confidence interval.

Now considering that the sample mean listing price was $310,000 for 4000 houses in the Northeastern region and $3,900 margin of error, it can be informed with 95 % confidence that the true mean listing price of the houses in Northeastern region lies between $306,100 and $313,900.

It can be concluded by saying that a narrower confidence interval is better than a wider interval when the focus is to increase the accuracy for the estimate of mean listing price of houses in Northeastern region. Also, analysis revealed that the mean listing price of houses in Northeastern region lied between $306,100 and $313,900.

Answer the following questions:

Some good thoughts in recommending the gold package. What about comparing the MOEs of the 3? Why not recommend one of the other packages to the client?