Course Project - Phase 3 Option 2 (Patients at NLEX hospital):
Phase 2
Phase 2
Lucia Ruiz
Rasmussen College
Author Notes
This paper is being submitted on February 26, 2017 for Juton Hemphill’s Inferential Statistics and Analytics course.
In the statistical inference, the main aim is to estimate the populations’ parameters by the use of samples that have been drawn from that population.
There is thus the need to create a confidence interval. It gives the range values that have a chance of including unknown parameters from the population from the sample drawn (2017). Simply this means that when drawing an inference from a sample taken we have the estimate of the population parameter and the margin of error which means there is a chance of inclusion of unknown population parameter, the estimated range being calculated from a given set of sample data (DG, 2017).
The point estimate of a population parameter is a single value used to estimate the population parameter. For example, the sample mean x is a point estimate of the population mean μ. Point estimation is defined as the process by which the estimation of parameters from a normal probability distribution that is based on the data that is observed from a particular population.
The mean is the best point estimator. It is because the mean in a normal distribution is the average of the data set and normally the center of the data. It is where most of the items in the population lie and usually represent the data set. For all populations, the sample mean x is an unbiased estimator of the population mean µ, meaning that the distribution of sample means tends to center about the value of the population mean µ. For most populations, the distribution of sample means x is always more consistent (with less variation) than the distributions of other sample statistics.
The confidence interval that is created from a range based on a confidence level and useful in the estimating the actual population values based on the normal distribution for a statistic of that population. It is useful to accommodate a range of estimates and reduce chances of avoiding of misinterpretation of non-significant results of small studies ("Point Estimates and Confidence Intervals", 2017).
Since the best point estimator of the population means is the sample mean x is a point estimate of the population mean μ then for our data, then the Mean = 3705 / 60 = 61.81667 is the best.
At 95% confidence level
)
)
59.26 < x < 64.38
At 99% confidence level
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)
58.45 < x < 65.18
Interpretation: at 95% confidence level we estimate the populations mean to be 61.82. We are 95% confident that the true value of the mean lies between 59.26 < x < 64.38. From our study of the patients infected with the infectious disease in NCLEX Memorial Hospital is that at 95% confidence interval the mean lies between 59.26 < x < 64.38.
On the other hand, at 99% confidence level, we estimate the populations mean to be 61.82. We are 95% confident that the true value of the mean lies between 58.45 < x < 65.18. From our study of the patients infected with the infectious disease in NCLEX Memorial Hospital is that at 99% confidence interval the mean lies between 58.45 < x < 65.18.
Conclusion
When the confidence level increases, the confidence interval increases. The increase of the confidence level from 95% to 995 leads to the range increase. A higher percent confidence level gives a wider band. The accommodation of a wide range in the interval leads to the chance of an error occurring form the interval of the means. Though there is more uncertainty, there is less chance of making an error but there is more uncertainty.
Reference
(2017). Retrieved 26 February 2017, from http://stattrek.com/statistics/dictionary.aspx?definition=confidence_interval
DG, A. (2017). Why we need confidence intervals. - PubMed - NCBI. Ncbi.nlm.nih.gov. Retrieved 26 February 2017, from https://www.ncbi.nlm.nih.gov/pubmed/15827844
Point Estimates and Confidence Intervals. (2017). Cliffsnotes.com. Retrieved 26 February 2017, from https://www.cliffsnotes.com/study-guides/statistics/principles-of-testing/point-estimates-and-confidence-intervals
