MATH 225 Week 7 Assignment: Lab
Student Name
Chamberlain University
MATH-225 Statistical Reasoning for the Health Sciences
Prof. Name
Date
Week 7 Lab Assignment
Summary of Learning from the Articles
The assigned readings provided valuable insight into the importance and application of confidence intervals (CIs) within the health sciences. Confidence intervals are a statistical tool used to estimate a range where the true value of a population parameter is likely to fall, based on sample data. A 95% CI is particularly common in health research, suggesting that if multiple samples were taken and intervals calculated, 95% of them would capture the true parameter. This method helps researchers determine the precision and reliability of their data. A narrow CI reflects more accurate estimates, often due to a larger sample size or low variability, while a wide CI indicates potential issues with sampling or data spread. Additionally, when CIs for two different groups do not overlap, researchers can infer a statistically significant difference between them. Overall, understanding and applying CIs allows healthcare professionals to interpret data more critically and make better evidence-based decisions regarding treatment, policy, and patient care.
Data Collection
The data used in this analysis include 20 height measurements—10 were collected personally, and 10 were provided by the instructor during Week 5.
Preliminary Calculations
| Statistic | Value |
|---|---|
| Sample Mean | 58.93 |
| Standard Deviation | 8.23 |
| Your Height | 65 |
Method of Data Collection
1. What method of collection did you use for your data?
The data collected for this lab were obtained through convenience sampling. This technique involves selecting participants who are easily accessible and willing to participate. In my case, I collected height data from 10 students who were nearby and available, without any form of random selection.
2. What are some faults with this type of data collection?
Convenience sampling has several limitations. First, it introduces selection bias because the sample may not accurately reflect the diversity of the broader population. Individuals who are conveniently available may share similar characteristics, limiting variability. Second, findings from such a sample have limited generalizability. This means the conclusions drawn may not apply to the overall population due to the homogeneity or skewed nature of the sample.
3. What other types of data collection could you have used, and how might this have affected your study?
Alternative methods such as simple random sampling or systematic sampling could have improved the representativeness of the data. In simple random sampling, every individual has an equal chance of being selected, reducing bias and enhancing the reliability of findings. In systematic sampling, one might select every nth person from a list, providing structure while still approximating random selection. Both approaches would produce more generalizable and statistically valid results, strengthening the credibility of the analysis.
Calculation of 95% Confidence Interval
1. What is your point estimate, and what does this mean?
The point estimate for the average height of individuals at my workplace is 58.93 inches, which represents the sample mean of the collected data. This value is considered the best approximation of the true average height within the population. However, as an estimate, it is subject to sampling variability and may not exactly match the true population mean.
2. What is the 95% confidence interval for the true mean height?
| Calculation Step | Result |
|---|---|
| Sample Mean (x̄) | 58.93 inches |
| Standard Deviation (s) | 8.23 inches |
| Sample Size (n) | 20 |
| Standard Error (SE) | 1.84 |
| z-value (95% CI) | 1.96 |
| Margin of Error (ME) | 3.61 |
| Confidence Interval (CI) | (55.32, 62.54) |
3. Practical interpretation of the 95% confidence interval
Based on the sample, we can say with 95% confidence that the true average height of people in my workplace is between 55.32 inches and 62.54 inches. This means if we repeated this sampling method many times, approximately 95% of the resulting confidence intervals would contain the true population mean.
Calculation of 99% Confidence Interval
1. What is the 99% confidence interval for the true mean height?
| Calculation Step | Result |
|---|---|
| Sample Mean (x̄) | 58.93 inches |
| Standard Deviation (s) | 8.23 inches |
| Sample Size (n) | 20 |
| Standard Error (SE) | 1.84 |
| z-value (99% CI) | 2.576 |
| Margin of Error (ME) | 4.74 |
| Confidence Interval (CI) | (54.19, 63.67) |
2. Practical interpretation of the 99% confidence interval
We are 99% confident that the true average height of individuals at my workplace lies within the range of 54.19 inches to 63.67 inches. This wider interval reflects a greater level of certainty, although it also introduces more variability into the estimate.
Compare Margins of Error
1. Would the margin of error be larger or smaller for the 99% CI? Explain your reasoning.
The margin of error is larger for the 99% confidence interval compared to the 95% interval. This occurs because increasing the level of confidence requires capturing a broader range of values, which is achieved by increasing the z-score. The higher z-score (2.576 vs. 1.96) results in a wider interval and thus a larger margin of error.
2. As the confidence level increases, what happens to the Margin of Error?
As the confidence level increases, the margin of error also increases. This is because a higher confidence level requires a wider interval to ensure the population mean is captured more reliably. Although this improves the certainty of the estimate, it may reduce the precision of the result.
Final Instructions
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References
Cumming, G., & Calin-Jageman, R. J. (2016). Introduction to the new statistics: Estimation, open science, and beyond. Routledge.
Frost, J. (2021). Statistics by Jim: Confidence Intervals Explained. https://statisticsbyjim.com
MATH 225 Week 7 Assignment: Lab
Pagano, M., & Gauvreau, K. (2018). Principles of biostatistics (2nd ed.). Cengage Learning.