G310 Advanced Statistics And Analytics Option 2 Intro 953181

G310 Advanced Statistics And Analytics Option 2introductionas A Hea

As a healthcare professional, you will work to improve and maintain the health of individuals, families, and communities in various settings. Basic statistical analysis can be used to gain an understanding of current problems. Understanding the current situation is the first step in discovering where an opportunity for improvement exists. This course project will assist you in applying basic statistical principles to a fictional scenario in order to impact the health and wellbeing of the clients being served. This assignment will be completed in phases throughout the quarter.

Scenario: You are currently working at NCLEX Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. You believe that the ages of these patients play a critical role in the method used to treat the patients. You decide to speak to your manager and together you work to use statistical analysis to look more closely at the ages of these patients. You do some research and put together a spreadsheet of the data that contains the following information:

• Client number
• Infection Disease Status
• Age of the patient

The data set consists of 60 patients that have the infectious disease with ages ranging from 35 years of age to 76 years of age for NCLEX Memorial Hospital. The data has been analyzed using various statistical measures, including measures of center and variation, and confidence intervals, to understand the distribution of ages among infected patients.

Classification of the Variables

The ages are quantitative variables, providing numerical data where the quantity of years is the focus. These can be viewed as discrete because they are whole numbers but also as continuous because age varies for each patient. Patient numbers are discrete variables, incrementing uniformly and serving as identifiers.

Measures of Center

Key measures include:

• The mode, which indicates the most frequently occurring age among patients.
• The median, which is the middle age value when data are ordered.
• The mean (average), calculated as the sum of all ages divided by the total number of patients, providing a central value—here, approximately 61.82 years.
• The midrange, which is the average of the minimum and maximum ages, indicating a midpoint in the data (here, 20.5 years).

Measures of Variation

Important measures include:

• The range, representing the difference between the maximum (76) and minimum (35) ages, which is 41 years.
• The interquartile range (IQR), which indicates the spread of the middle 50% of ages.
• The standard deviation, measuring the average distance of ages from the mean; in this data, it is approximately 8.92 years.
• The variance, the square of the standard deviation, approximately 79, indicating the data spread squared.

Analysis and Interpretation

The analysis shows that most patients affected by the infectious disease are around 61 years old, with ages ranging from 35 to 76 years. This suggests that older adults within this age range are more susceptible or are the primary demographic affected in this scenario. The standard deviation indicates that ages vary reasonably around the mean, with most patients' ages clustering near 61 years, yet some outliers extend from young to older ages.

Constructing Confidence Intervals for the Population Mean

Confidence intervals estimate the range within which the true population mean age of all patients with the infectious disease is likely to fall. They are critical for understanding the precision of the sample mean as an estimate of the population mean, especially when direct measurement of the entire population is not feasible.

The point estimate is the sample mean, which is approximately 61.82 years. To construct confidence intervals, the standard deviation (approximately 8.92 years) and the sample size (n=60) are used, along with the critical z-values corresponding to confidence levels of 95% and 99%.

For a 95% confidence level:

• The standard error of the mean (SE) is calculated as 8.92 / √60 ≈ 1.15.
• The critical z-value is 1.96.
• The margin of error (ME) is 1.96 × 1.15 ≈ 2.25.
• The confidence interval is approximately 61.82 ± 2.25, or (59.57, 64.07) years.

For a 99% confidence level:

• The critical z-value is 2.576.
• The margin of error is 2.576 × 1.15 ≈ 2.96.
• The confidence interval approximates 61.82 ± 2.96, or (58.86, 64.78) years.

Comparison of Confidence Intervals

The 95% confidence interval is narrower, reflecting a smaller range where the true mean likely falls, with 95% certainty. Increasing the confidence level to 99% widens the interval, providing greater assurance that the population mean is within this range, but at the expense of precision. This illustrates the trade-off between confidence level and interval width: higher confidence levels result in broader intervals.

Conclusions

Descriptive statistics reveal that ages of infected patients tend to cluster around 61 years, with variation captured by the standard deviation and range. Constructing confidence intervals demonstrates that the true average age of all infected patients likely falls within approximately 59.57 to 64.07 years at 95% confidence, and 58.86 to 64.78 years at 99% confidence. These estimates support targeted approaches in treatment planning, emphasizing age-related susceptibilities.

Understanding the distribution and range of patient ages helps inform resource allocation and tailored medical intervention strategies. The variability measures emphasize the importance of considering outliers and age spread when designing treatment protocols and implementing prevention measures for vulnerable age groups.

References

• Triola, M. F. (2012). Elementary Statistics (12th ed.). Boston: Pearson.
• Smithson, M. (2003). Confidence Intervals. Thousand Oaks, CA: Sage Publications.
• Albright, S. C., Winston, W. L., & Zappe, C. J. (2011). Data Analysis and Decision Making. Mason, OH: South-Western/Cengage Learning.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2014). Introduction to the Practice of Statistics (8th ed.). New York: W. H. Freeman.
• Schneider, A. (2020). Applied Statistics for Healthcare Professionals. New York: Routledge.
• Wackerly, D., Mendenhall, W., & Scheaffer, R. (2008). Mathematical Statistics with Applications. Boston: Cengage Learning.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
• Laerd Statistics. (2020). Confidence Intervals. Retrieved from https://statistics.laerd.com/statistical-guides/confidence-intervals-statistics.php
• Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied Statistics for the Behavioral Sciences. Boston: Houghton Mifflin.
• Fisher, R. A. (1925). Statistical Methods for Research Workers. London: Oliver & Boyd.