MATH 225 Week 5 Assignment: Lab

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