Estimating House Listing Prices- Confidence in the $310,000 Mean and Margin of Error Analysis
Formulate a recommendation and write a confidence statement in the context of this scenario
One way to estimate the range of value for further analysis purposes is by formulating a confidence interval that offers a basis for a recommendation. After conducting extensive research, I thought the second package could be helpful to the business. The sample mean of the house prices was taken as $310,000.
A 95% confidence interval is to determine where the prices of the houses in the Northeast area lie. Using the sample confidence interval formula, we are 95% confident that the true mean listing price of the houses in the Northeast is between [$302,000, 318,000].
To come up with a criterion for choosing the mean housing prices in the Northeast region, the sample can be used for the estimation of the mean. The accuracy of the estimated value depends on the confidence level used (Glen, 2019). For a 95% confidence level, the values obtained have a larger deviation from the real value compared to a 99% confidence interval. Therefore, the interval under which the mean listing price would lie becomes narrow with the increase in the confidence level. Also, the confidence range depends on the sample size used in relation to the population under interest. As the sample size increases, the confidence range becomes smaller; thus, the estimated values are closer to the true mean.
Explain the factors that went into your recommendation, including a discussion of the margin of error
The confidence interval for the mean listing price is calculated based on the error margin. The sample size determines the margin of error (Glen, 2019). As the sample size increases, the margin of error decreases. Subsequently, a large margin of error will lead to larger confidence intervals and vice versa. It is recommendable that the company considers package 2. Although the package has higher expenses in data collection, the smaller margin of error will enable the company to formulate better models, thus recovering from the data collection expenses. With a more accurate confidence interval, the company’s agents can work accurately with a smaller price interval. Although the data collection expenses in package 1 are the least expensive, the margin of error is high, which may cause greater variations in listing prices from the true mean. This could consequently affect the company’s decision-making process. The third package has the greatest service cost, although the margin error is still high. Therefore, package 2 fits the company’s housing decisions.
References
Glen, S. (2019). “Confidence Interval: How to Find it: The Easy Way!” From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/probability-and-statistics/confidence-interval/
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Question 
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 all packages.
Estimating House Listing Prices- Confidence in the $310,000 Mean and Margin of Error Analysis
“I am [#] % confident the true mean . . . [in context].”
Explain the factors that went into your recommendation, including a discussion of the margin of error