MATH 225 Week 6 Discussion: Confidence Intervals

Student Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name:

Date

Confidence Intervals

A confidence interval (CI) is a range of values surrounding a sample statistic, such as a mean or proportion, that helps determine if the same results can be expected when a study or intervention is repeated. It addresses the precision of study findings, with narrower CIs offering greater confidence that results are reproducible. For example, a systematic review on the effect of tai chi on sleep quality in older adults might find a lower boundary of 0.49, a sample statistic of 0.87, and an upper boundary of 1.25 for the CI. This narrow range suggests that tai chi significantly improves sleep quality and that the findings are unlikely to be due to chance. Because the CI does not include zero (indicating no effect), clinicians could confidently include tai chi exercises in treatment recommendations for patients with sleep difficulties. Understanding CIs equips healthcare professionals to design studies and make informed decisions about patient care based on reliable evidence.

Application of Confidence Intervals in Healthcare

Variables tracked in healthcare, such as blood glucose levels, can be analyzed using confidence intervals to improve patient care. For instance, blood glucose control is vital in managing critically ill patients. By comparing various glucose control algorithms, a 95% confidence interval could help determine which algorithm offers the most reliable control. Suppose a sample of 30 patients using one algorithm has a mean glucose level of 111, with a 95% CI ranging from 102 to 120. This suggests that 95% of patients using this algorithm will likely have glucose levels within that range. These findings can help healthcare facilities choose the most effective glucose control strategies, ensuring better outcomes for patients.

Altering the confidence level affects the width of the CI. A 90% CI is narrower and less conservative, while a 99% CI is wider and more cautious. The choice of confidence level depends on the study’s purpose. For critical decisions, a 99% CI might be preferred, whereas a 90% CI could suffice for preliminary analyses. Presenting findings to decision-makers in healthcare requires clarity, emphasizing how improved glucose control algorithms could lead to better patient outcomes and operational efficiency.

Table: Confidence Intervals Overview

Topic	Description	Example
Definition	Range of values around a sample statistic indicating expected reproducibility of study results.	Narrow CI suggests high precision; broad CI indicates less certainty.
Healthcare Application	Used to evaluate variables like blood glucose levels to identify optimal care strategies.	A 95% CI of 102–120 for glucose levels suggests reliable control using a specific algorithm.
Impact of Confidence Levels	Higher confidence levels (e.g., 99%) increase interval width, affecting data utility and decision-making.	A 99% CI might range from 90–130, providing broader but less actionable insights.

References

Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory to Business Statistics. OpenStax. Retrieved from https://openstax.org/details/books/introductory-business-statistics