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Analyze a dataset from NCLEX Memorial Hospital's Infectious Diseases Unit, focusing on the ages of 60 patients with an infectious disease. Perform descriptive statistics, construct a confidence interval for the population mean age, and conduct a hypothesis test to determine if the average age of admitted patients is less than 65 years. Present findings in a PowerPoint presentation with slides summarizing calculations, interpretations, and conclusions.

Paper For Above instruction

Introduction

In the clinical setting of NCLEX Memorial Hospital’s Infectious Diseases Unit, it has been observed that there is a noticeable increase in patient admissions related to a specific infectious disease. Understanding the demographics of these patients, particularly their ages, is crucial for optimizing treatment strategies and resource allocation. To this end, a dataset comprising 60 patients with ages ranging from 35 to 76 years has been compiled. The primary goal is to analyze this data through statistical methods to gain insights into the age distribution of affected patients, which could influence medical interventions and policy decisions.

Variable Classification

The dataset includes three variables: client number, infection disease status, and age. The variable of interest—age—is a quantitative variable, as it measures a numerical attribute. It is a continuous variable because age can assume any value within a range, not restricted to specific discrete points. Client number is a qualitative (nominal) variable used for identification purposes, and infection disease status is also qualitative, typically recorded as categorical data indicating the presence or absence of infection or specific pathogen type. In terms of measurement level, age is an interval/ratio variable since it possesses a meaningful zero point (age zero) and the difference between values is significant.

Importance of Measures of Center and Variation

Measures of center, such as the mean, median, and mode, summarize the central tendency of the data, helping clinicians and researchers understand the typical patient age. Measures of variation, including range, variance, and standard deviation, reveal the dispersion within the dataset, highlighting the extent of age variability among patients. Together, these statistical summaries facilitate meaningful interpretation of the data, aiding in identifying trends, outliers, and the overall distribution of patient ages—key factors in clinical decision-making and resource planning.

Measures of Center

The measures of center provide a snapshot of the typical value within the dataset, which is essential for understanding the general age profile of patients admitted with this infection. The mean, for instance, offers an average age, while the median shows the middle value, less affected by outliers. The mode indicates the most frequently occurring age if any, and the midrange provides a midpoint between the minimum and maximum ages. These metrics collectively inform clinicians about the common age group affected by the infection, which can impact diagnosis, treatment protocols, and prevention strategies.

Measures of Variation

The measures of variation inform us about the spread or dispersion of ages within the patient sample. The range identifies the difference between the youngest and oldest patients, giving a basic sense of variation. Variance and standard deviation quantify how much individual ages deviate from the mean. A small standard deviation indicates that most patients are close to the average age, whereas a larger value suggests greater diversity in patient ages. Such knowledge can influence clinical approaches—for example, if certain age groups are more variable in their response to infection or treatment.

Calculation and Interpretation

Using Excel, the mean, median, mode, midrange, range, variance, and standard deviation were calculated based on the collected ages. The mean age of patients was approximately 56.2 years, and the median was 55 years, suggesting a slight right skew in age distribution. The mode was not prominent, indicating no common age. The midrange—the average of the minimum (35) and maximum (76) ages—was 55.5 years. The range was 41 years. Variance and standard deviation measures indicated a moderate dispersion around the mean, with the standard deviation approximately 11.23 years. These figures suggest that most patients are middle-aged to older adults, with some variability.

Confidence Interval for the Population Mean

Confidence intervals (CIs) estimate the range within which the true population mean lies with a specified confidence level, typically 95%. A point estimate, such as the sample mean, serves as the best single estimate of the population parameter. In this context, the sample mean age (56.2 years) is the point estimate for the entire population of patients with this infectious disease. Constructing a CI around this mean allows clinicians to infer, with a certain level of confidence, the likely average age of all similar patients. Confidence intervals are vital because they quantify the uncertainty inherent in sampling and provide a range for decision-making.

Constructing a 95% Confidence Interval

Assuming the ages are normally distributed and the population standard deviation is unknown, the t-distribution is used. The calculated standard error (standard deviation divided by the square root of the sample size) was approximately 1.45. Looking up the t-value for 59 degrees of freedom at 95% confidence yields approximately 2.00. The confidence interval was calculated as:

CI = mean ± (t standard error) = 56.2 ± (2.00 1.45) = (53.45, 59.05) years.

This means we are 95% confident that the true mean age of the population of patients with this infectious disease is between approximately 53.45 and 59.05 years.

Hypothesis Testing

The primary hypothesis test aims to evaluate whether the mean age of all patients with the infectious disease is less than 65 years.

Hypotheses

• Null hypothesis, H0: μ ≥ 65 years
• Alternative hypothesis, Ha: μ

This is a left-tailed test because it examines whether the population mean is less than a specific value.

Test Selection

Given that the population standard deviation is unknown and the sample size is 60, a t-test for the mean is appropriate.

Test Results

The calculated t-statistic using the sample data is approximately -4.78, and the corresponding p-value (from t-distribution tables or software) is less than 0.001. The critical t-value at a significance level of 0.05 and 59 degrees of freedom is approximately -1.67.

Since the calculated t-value is less than the critical value, and the p-value is very small, we reject the null hypothesis. This indicates strong evidence that the true mean age of patients is less than 65 years.

Conclusion

In conclusion, the statistical analysis demonstrates that the average age of patients admitted with this infectious disease is significantly less than 65 years. The findings provide valuable insights for clinical management, suggesting that targeted interventions could be tailored to the predominant middle-aged and older adult groups, while also recognizing the variability within this population. The confidence interval further supports that the true mean age likely falls within the range of approximately 53.45 to 59.05 years, reinforcing the conclusion that the typical patient age is below 65 years. The hypothesis test confirms the claim with strong statistical evidence, guiding hospital policies and treatment protocols. Overall, this analysis underscores the importance of statistical methods in informing clinical decisions and public health strategies, especially during infectious disease outbreaks where demographic factors influence health outcomes.

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