MATH 225 Week 8 Final Exam

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Independent Variables in Regression Analysis of BMI

Regression analysis serves as a valuable tool in examining the relationship between one or more independent variables and a continuous dependent variable. In the case of body mass index (BMI), potential independent variables include total cholesterol levels measured in milligrams per deciliter (mg/dL), age, and gender. Each of these variables can influence BMI in various ways. For instance, total cholesterol intake may correlate with body fat and overall health, age can reflect metabolic changes, and gender often impacts body composition and fat distribution (Creswell & Creswell, 2018).

Although BMI is a useful indicator of body weight relative to height, it has limitations, as it does not differentiate between fat, muscle, or bone mass and does not indicate fat distribution within individuals. Nonetheless, understanding how cholesterol intake, age, and gender relate to BMI provides a comprehensive overview of the factors that can affect this measurement (Centers for Disease Control and Prevention, 2015).

The correlation coefficient is a critical statistic that demonstrates the strength and direction of the relationship between BMI and the chosen independent variables. This statistic can be calculated using statistical software like Excel or SPSS. A strong, positive correlation would indicate that as one variable increases, so does BMI, while a negative correlation would suggest an inverse relationship. These insights are essential for interpreting how various factors impact BMI, as emphasized by Holmes, Illowsky, and Dean (2018).

Summary of Key Points

References

Centers for Disease Control and Prevention. (2015). Body mass index: considerations for practitioners. Retrieved from https://www.cdc.gov/obesity/downloads/bmiforpactitioners.pdf

Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Thousand Oaks, CA: Sage.

MATH 225 Week 8 Final Exam

Holmes, A., Illowsky, B., & Dean, S. (2018). Introductory business statistics. Houston, TX: OpenStax.

MATH 225 Week 7 Assignment: Lab

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Sampling Methods

The sampling method employed for the Week 5 lab assignment to collect height data was convenience sampling. This non-random sampling technique relies on data or samples that are easily accessible. However, convenience sampling can introduce bias, favoring certain outcomes over others. A significant limitation of this method is that a convenience sample does not adequately represent the entire population, potentially leading to systemic bias. Alternatively, systematic sampling could have been utilized to gather the data. Systematic sampling is a straightforward method in which the researcher randomly selects a starting point and subsequently collects every nth data point from the population. This approach is considered true random sampling and offers a better representation of the overall population.

Statistical Analysis

The following statistical data summarizes the findings from the collected height data:

A point estimate is the process of determining an approximate value of a parameter, such as the mean or average of a population derived from random samples. In this analysis, the point estimate for the height data is 66.1 (Encyclopedia Britannica, 2019).

Confidence Intervals

To calculate the confidence intervals for the true mean height of individuals at my workplace, the confidence interval is defined as a range of values that indicates the probability that the parameter lies within it. For the height data collected, the confidence interval’s lower limit is 65.1 inches, while the upper limit is 67.1 inches.

A practical interpretation of this interval indicates that I am 95% confident the true mean height of all employees in my company falls between 65 inches and 67 inches. When evaluating a 99% confidence interval for the same data, the following statistics were obtained:

The margin of error for the 99% confidence interval is larger than that of the 95% confidence interval, indicating greater uncertainty. This wider range suggests that the true population mean is more likely to be included within this interval, while the 95% confidence interval carries a 5% chance that the population mean lies outside it.

References

Encyclopedia Britannica. (2019). Point Estimate. Retrieved from Encyclopedia Britannica

MATH 225 Week 7 Assignment: Lab

MATH 225 Week 6 Discussion: Confidence Intervals

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Confidence Intervals

In simple terms, a confidence interval (CI) represents a range of values surrounding a sample statistic, such as a mean or proportion. This interval indicates where clinicians can expect to find similar results if they replicate the study’s protocol or intervention, including the same outcome measurements. When considering whether research findings can be applied to practice, it is crucial to evaluate their precision, which is reflected in the confidence interval. A narrow CI around a sample statistic suggests a high degree of reliability, meaning the results can be expected to remain consistent across different implementations of the research.

For instance, consider a systematic review that examines the impact of tai chi on sleep quality in older adults. If the analysis yields a lower boundary CI of 0.49, a study statistic of 0.87, and an upper boundary of 1.25, this indicates that each limit is 0.38 units away from the sample statistic, reflecting a relatively narrow CI. The calculation (UB + LB)/2 = Statistic results in (1.25 + 0.49)/2 = 0.87. It’s important to note that a mean difference of 0 signifies no difference, and since this CI does not encompass 0, the sample statistic is statistically significant and unlikely to arise by chance. Given that the systematic review supports tai chi as beneficial for sleep, clinicians can confidently recommend tai chi exercises to patients experiencing sleep difficulties based on these findings.

Initial Post Instructions

Reflecting on the various variables tracked by healthcare facilities, confidence intervals can be generated for population parameters such as means or proportions derived from these variables. Select a topic of study relevant to your workplace, describe the chosen variable and parameter (mean or proportion), and explain your rationale for creating an interval that captures the true parameter value with 95% confidence. Consider how adjusting the confidence interval to 90% or 99% might influence the study outcomes and which level (90%, 95%, or 99%) is most appropriate based on the selected study type. Additionally, contemplate how the study results could be presented to management in a bid to drive change within the organization.

References

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

MATH 225 Week 6 Discussion: Confidence Intervals

Kelly, T. M., Jensen, R. L., & Robinson, M. K. (1988, Nov/Dec). Method for estimating confidence levels for measurements by blood glucose monitoring. Diabetes Care, 11(10), 808-812. Retrieved from https://chamberlainuniversity.idm.oclc.org/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=edb&AN=72335516&site=eds-live&scope=site

MATH 225 Week 5 Assignment: Lab

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Week 5 Lab Assignment

For this study, the heights of 10 female friends were collected. The sample used is considered a biased, convenience sample since all participants were friends who verbally provided their height instead of being physically measured. The heights recorded were as follows: 5’4” (64 inches), 5’4” (64 inches), 5’5” (65 inches), 5’5” (65 inches), 5’6” (66 inches), 5’6” (66 inches), 5’6” (66 inches), 5’7” (67 inches), 5’7” (67 inches), and 5’9” (69 inches). Using Excel, the mean height was calculated to be 65.9 inches, with a sample standard deviation of 1.5239. Additional calculations indicated that the sample variance was 2.3222, the population variance was 2.0900, and the population standard deviation was 1.4457.

In comparing my height to the mean of this group, I am shorter. I am 5’3” (63 inches), while the mean height of my group is 65.9 inches, indicating that I fall below the average height of the group. The sampling method used was a convenience sample, chosen based on the ease of contacting friends via a group text message due to COVID-19 restrictions. This method inherently introduces bias since the data are not randomly selected. The study was conducted in Sacramento, California, with participants aged between 29-35 years. The sample consisted of only females, and most were Caucasian, with two participants being Hispanic. Interestingly, the two Hispanic women were the shortest in the group, though I remained the shortest overall. Another noteworthy factor is that some participants provided their heights with uncertainty, such as “I think I’m around 5’6”,” which introduces further bias into the data.

Using the Empirical Rule, the distribution of heights was analyzed. The rule suggests that 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% within 3 standard deviations. For this dataset, 68% of the women were between 64.4 and 67.4 inches tall, 95% between 62.9 and 68.9 inches tall, and 99.7% between 61.3 and 70.5 inches tall. As my height is 63 inches, I fall in the lower 2.84% of the population, meaning 97.15% of the population is taller than me.

Row and Columns Table

Empirical Rule Distribution

References

Glen, S. (2020, September 20). Empirical Rule (68-95-99.7) & Empirical Research. Retrieved October 02, 2020, from https://www.statisticshowto.com/empirical-rule-2/

MATH 225 Week 5 Assignment: Lab

Holmes, A., Illowsky, B., & Dean, S. (2019). Introductory Business Statistics (4.0). Retrieved from https://openstax.org/details/books/introductory-business-statistics

MATH 225 Week 4

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

MATH 225 Week 3 Discussion – Central Tendency and Variation

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Discussion: Central Tendency and Variation

Holmes, Illowsky, and Dean (2019) define central tendency as the measure of an average, represented by the mean, median, and mode, which summarize the center of a data set. Variation, on the other hand, refers to the extent to which the data is spread out and includes metrics like range, variance, and quartiles.

For this discussion, I collected pulse rates from 10 registered female nurse case manager senior analysts, who make home visits weekly. The pulse rates were as follows: 68, 98, 66, 82, 94, 70, 78, 82, 86, and 92. The mean pulse rate was 81.6, and the median was 82, as determined by arranging the data in ascending order. The mode, which appears most frequently, was also 82. The sample variance was 125.155, and the standard deviation was 11.187. No outliers were observed, with values ranging from 66 to 98.

Wong et al. (2012) highlight that ensuring consistency in data collection, such as measuring pulse rates at the same location, can prevent skewed results. In my case, factors like activity levels or stress might have affected the pulse rates, and a more standardized measurement process could improve the accuracy of the data. Establishing clear criteria for data collection would help ensure comparability, as the saying goes, “compare apples to apples.”

Table: Summary of Statistical Concepts

References

Wong, J., Lu, W., Wu, K., Liu, M., Chen, G., & Kuo, C. (2012). A comparative study of pulse rate variability and heart rate variability in healthy subjects. Journal of Clinical Monitoring and Computing, 26(2), 107-114. doi:http://dx.doi.org/10.1007/s10877-012-9340-6

MATH 225 Week 3 Discussion – Central Tendency and Variation

MATH 225 Week 2 Discussion: Graphing and Describing Data in Everyday Life

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Discussion: Graphing and Describing Data in Everyday Life

To represent injury data collected from a clinic over a month, I would use a relative frequency table. As per Chamberlain (2019), a relative frequency table displays the percentage of data points that fall into each category, with the sum of all frequencies equaling 100%. This data can be visually represented using a horizontal bar chart. The injuries would be displayed along the vertical axis, while the number of people sustaining those injuries would be shown along the horizontal axis.

For the second data set, which tracks patient waiting times at a doctor’s office, I would use a frequency table. According to OpenStax (2019), a frequency table indicates the number of occurrences for each data value, with the total representing the sample size. In this case, the waiting times would appear in the first column, while the number of patients experiencing those wait times would be listed in the second. Using these data visualization methods can help in understanding the distribution of injuries and patient waiting times more effectively. Higgins, Simpson, and Johnson (2018) emphasize that big data analysis in nursing can generate new knowledge and improve patient care. Understanding statistical analysis in nursing can help improve work environments and patient outcomes through evidence-based practices.

References

Chamberlain University. (2019). Week 2 Lesson: Graphing and describing data. Retrieved from https://chamberlain.instructure.com/courses/47052/pages/week-2-lesson-graphing-and-describing-data?module_item_id=6093071

Higgins, M., Simpson, R. L., & Johnson, W. G. (2018). What about big data and nursing? Statistics, computer science, and nursing work together to analyze data and inform patient care. American Nurse Today, 13(5), 29–31. Retrieved from https://searchebscohost-com.chamberlainuniversity.idm.oclc.org/login.aspx?direct=true&db=ccm&AN=129530313&site=eds-live&scope=site

MATH 225 Week 2 Discussion: Graphing and Describing Data in Everyday Life

OpenStax CNX. (2019). Introductory business statistics. Retrieved from https://cnx.org/contents/tWu56V64@35.8:UMM7d-Hy@19/2-1-Display-Data

MATH 225 Week 1 Discussion: Basic Statistics Data Used in Everyday Life

Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name

Date

Discussion: Basic Statistics Data Used in Everyday Life

According to Holmes, Illowsky, and Dean (2019), statistics play an essential role in our daily lives. For this discussion, I will focus on the long-term effects of intentional weight loss on diabetes and hypertension. Both diabetes and hypertension are quantitative data as they can be measured numerically. The study employed weights and blood pressure readings, which are continuous variables since they can take any value within a reasonable range. In contrast, qualitative data would encompass attributes like blood type or ethnicity, which are non-numerical in nature.

The research utilized a stratified sampling approach by dividing the population into subgroups—those undergoing surgical treatment versus those receiving conventional treatment. The researchers initially included 480 primary healthcare centers, collecting data from 2000 patients in each group and eventually narrowing the sample to 346 patients in each group. After eight years, the study found that the group utilizing non-pharmacological weight loss methods did not observe improvements in weight, diabetes, or blood pressure. However, those who underwent weight loss surgery experienced significant weight loss and a reduction in diabetes cases by one-fifth, though blood pressure improvements were not sustained despite a 16% reduction in body weight.

References

Holmes, A., Illowsky, B., and Dean, S. (2019) Introductory Business Statistics. Retrieved from http://cnx.org/contents/b56bb9e9-5eb8-48ef-9939-88b1b12ce22f Sjöström

MATH 225 Week 1 Discussion: Basic Statistics Data Used in Everyday Life

CD; Peltonen M; Wedel H; Sjöström L. (2000). Differentiated long-term effects of intentional weight loss on diabetes and hypertension. Retrieved from https://www.ahajournals.org/doi/full/10.1161/01.HYP.36.1.20