UNIT 1: Written Assignment

HS 4241 - 01 Psychopathology and Mental Health - UNIT 1 Written Assignment Instructor: Pankaj Mehrotra Date: 02/02/2025 QUESTION 1 ● Number of past road accidents → Ratio, Discrete It has a true zero (no accidents mean zero), and differences between values are meaningful. ● History of past road accident (Yes/No) → Nominal It categorizes individuals into groups without a specific order. ● Heartbeats per minute → Ratio, Continuous It has a true zero (no heartbeat means death), and it can take fractional values. ● Time taken to complete a race → Ratio, Continuous It has a true zero (zero time means the race hasn’t started), and it can take decimal values. ● Race (ethnicity) → Nominal It represents categories with no intrinsic order. ● ABO blood type → Nominal It represents distinct categories with no inherent ranking. ● Injury severity score (1 to 5 scale) → Ordinal The values have a meaningful order (higher scores indicate more severity), but the differences between them may not be equal. QUESTION 2 In this example, it appears that women are more likely to get the disease because the incidence rate (new cases) is seven times greater for women than for men. But since there are no sex-based differences in the prevalence rate (total cases at a given time), it suggests that women may have a shorter disease duration because of higher mortality or faster recovery. This could indicate that men contract the disease at a lower rate but live with it for a longer period of time, or that women heal faster and die at a higher rate. Another theory is that, while having a lower incidence, men may have a more chronic form of the disease that maintains an equivalent prevalence. QUESTION 3 I used Python to create a code to solve this exercise. # Define the sequences X = [1, -2, 4, -2, 0, 1] Y = [0.25, -0.5, 8, 2, 2, 5] Z = [2, 3, 6, 3, 1, 1] # Compute Σ (Xi * Yi * Zi^2) sum_product = sum(x * y * (z ** 2) for x, y, z in zip(X, Y, Z)) # Compute 2 * sqrt(sum_product) import math result = 2 * math.sqrt(sum_product) result And the result is approximately 67.26 QUESTION 4 ●​ Are the age groups mutually exclusive? Yes, since each participant only fits into one age group, the age categories are mutually exclusive. No one can be a member of two different age groups at the same time since they do not overlap. ●​ Is this sample representative of the age groups in city A? It's challenging to assess representativeness in city A without knowing the precise age distribution of the populace. It might not be entirely representative, though, given the small sample size (47 individuals). Furthermore, there are only two individuals in the older age categories (31 years or older), which may distort the results. ●​ How many males and females were included in the study? To find the number of females in each age group: 15 years or younger: 10×0.4=4 females 16-25 years: 25×0.6=15 females 26-30 years: 10×1.0=10 females 31 years or older: 2×1.0=2 females Total females = 4+15+10+2=31 To find the number of males: Total participants = 47 Total males = 47−31=16 ●​ Calculate the relative frequencies: Relative frequency = (Number of participants in each group) ÷ (Total participants) 15 years or younger: 10/47≈0.213 16-25 years: 25/47≈0.532 26-30 years: 10/47≈0.213 31 years or older: 2/47≈0.043 ●​ Does this data belong to descriptive or inferential statistics? Because it arranges and summarizes the sample's features without drawing conclusions about the broader population, this data falls under descriptive statistics. Without making any inferences outside of the sample, the table gives clear details on the participants' age distribution, gender proportions, and relative frequencies. REFERENCES: ●​ Illowsky, B. and Dean, S. (2017). Introductory Statistics. OpenStax Rice University. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). Retrieved from https://my.uopeople.edu/pluginfile.php/1954716/mod_page/content/3/TEXT%20intro ductory-statistics.compressed.pdf