MATH 225 Week 5 Assignment: Lab

MATH 225 Week 5 Assignment: Lab

Student Name

Chamberlain University

MATH-225 Statistical Reasoning for the Health Sciences

Prof. Name:

Date

Analyzing Height Data: A Statistical Perspective on Female Participants

When conducting statistical studies, the choice of participants, the method of data collection, and the analysis techniques used are critical factors. This article examines a study analyzing the height of 10 female participants, using statistical tools to draw insights from a convenience sample. Below, we explore the study design, key findings, and the challenges faced in the process.

Study Overview and Data Collection

The research focused on gathering the self-reported heights of 10 female friends. The study employed a convenience sampling method due to practical limitations, including restrictions caused by COVID-19. Participants shared their heights via text messages, introducing potential biases as no physical measurements were taken. This approach, while efficient, risks inaccuracies due to self-reported data.

Reported Heights (in inches):

• 64, 64, 65, 65, 66, 66, 66, 67, 67, 69

Demographic Details:

• Location: Sacramento, California
• Age Range: 29–35 years
• Gender: Female (100%)
• Ethnic Composition: Predominantly Caucasian (8 participants), with 2 Hispanic women.

Statistical Summary of the Data

Statistical analysis provides a clearer understanding of the collected data. Here are the calculated values:

• Mean (Average): 65.9 inches
• Median: 66.0 inches
• Mode: 66.0 inches (most frequent height)
• Range: 5.0 inches (difference between tallest and shortest)
• Sample Variance: 2.3222
• Sample Standard Deviation: 1.5239

These measures reveal that the data is relatively clustered, with a small variance and standard deviation indicating limited dispersion.

Interpreting Z-Scores and the Empirical Rule

A Z-score measures how far a data point is from the mean in terms of standard deviations. The Z-score for the researcher’s height (5’3” or 63 inches) was calculated as follows:

Z-Score Formula:
[ Z = \frac{(X – \text{Mean})}{\text{Standard Deviation}} ]

For ( X = 63 ):
[ Z = \frac{(63 – 65.9)}{1.5239} \approx -1.903 ]

This negative Z-score indicates that the researcher’s height is shorter than the group average. Based on the normal distribution:

• Probability Less Than 63 Inches: 2.84%
• Probability Greater Than 63 Inches: 97.15%

Using the Empirical Rule, we observe the following:

• 68% of Data: Falls within one standard deviation (64.4–67.4 inches).
• 95% of Data: Falls within two standard deviations (62.9–68.9 inches).
• 99.7% of Data: Falls within three standard deviations (61.3–70.5 inches).

Convenience Sampling and Its Limitations

The convenience sampling method was chosen due to its accessibility, but it presents notable limitations:

1. Bias Risk: The sample was not random, as it included only the researcher’s friends.
2. Data Accuracy: Self-reported heights may lack precision, with some participants providing approximate values.
3. Representation Issues: The sample is geographically and demographically narrow, limiting generalizability.

While convenience sampling is practical, especially during constraints like the COVID-19 pandemic, it compromises the study’s reliability and validity.

Key Observations and Findings

1. Researcher’s Height vs. Group Mean: At 5’3” (63 inches), the researcher’s height is significantly below the mean (65.9 inches), positioning her in the lower 2.84% of the population based on this sample.
2. Ethnic and Gender Homogeneity: The group’s composition lacked diversity, with a majority being Caucasian women from Sacramento, California.
3. Most Common Heights: Heights of 66 and 67 inches were prevalent, indicating a central tendency around these values.

Recommendations for Future Studies

To improve the validity and reliability of similar research, consider the following:

• Employ Random Sampling: Random selection reduces bias and ensures a more representative sample.
• Ensure Precise Measurements: Physically measuring participants’ heights eliminates inaccuracies in self-reported data.
• Expand Demographic Scope: Including participants from diverse locations, age ranges, and ethnicities enhances generalizability.

Conclusion

This study provides a fascinating glimpse into the statistical properties of a small, convenience-based sample. While limitations exist due to the methodology, the analysis effectively demonstrates the application of statistical concepts such as the mean, variance, and Z-scores. Future research can address these challenges to yield more robust and generalizable results.

References

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 5 Assignment: Lab

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