IOP2601 Assignment 2 Semester 1 Memo | Due 31 March 2025

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IOP2601 Assignment 2 Semester 1 | Due 31 March 2025. All questions answered. QUESTION 1 [10] 1.1 In your own words, briefly name and explain the first three steps of the research process. Provide examples where possible. (3) 1.2 In your own words, differentiate between descriptive statistics and inferential statistics. Provide examples where possible. (2) 1.3 Describe the differences or similarities between the mean, median and mode. (3) 1.4 Explain the characteristics of a normal distribution. (2) QUESTION 2 [7] Thabiso and Tshepo, twin siblings, are participating in a soccer betting competition with a chance to win R5 000 in cash prizes. The competition requires participants to bet on a winning team. Thabiso submitted 10 entries, while Tshepo submitted 15, contributing to a total of 500 qualifying entries. They are concerned about their chances of winning. Use this information to answer the following questions: 2.1 What is the probability that Thabiso will win the first prize? (2) 2.2 What is the probability that Tshepo will win the second prize if Thabiso wins the first prize? (Note: The winner of the first prize is not eligible for the second or third prize.) (2) 2.3 What is the probability that Thabiso and Tshepo will win the first and second prizes? (3) QUESTION 3 [19] Mental health challenges have become an increasing concern on university campuses worldwide, with many students experiencing stress, anxiety and depression due to academic pressure, social isolation and other factors. Regular physical activity is often promoted as a way of improving mental well-being. Numerous studies suggest that exercise can have a positive effect on people’s mental health by reducing stress, improving their mood and increasing their overall emotional resilience. In Pretoria, a group of research experts sought to investigate the relationship between lower physical activity and risk of depression among undergraduate students. Their study aimed to examine whether students with lower levels of physical activity (X) are likely to experience increased risk of developing depression and anxiety (Y). Use the data provided to answer the questions that follow. Participants (undergraduate students) Physical activity (X) Risk of depression/anxiety (Y) X² Y² XY N = 10 ƩX = 72 ƩX2 = 534 ƩY = 95 ƩY2 = 961 ƩXY = 682 ƩXƩY = 72 x 95 = 6840 (ƩX)2 = (72)2 = 5184 (ƩY)2 = (95)2 = 9025 3.1 Calculate the relationship between students’ engagement in physical activity (X) and their risk of developing depression and anxiety (Y). (3) 3.2 Interpret the correlation coefficient. (2) 3.3 What can you deduce about the nature of the relationship between the students’ physical activity (X) and their risk of developing depression and anxiety (Y)? (2) 3.4 Calculate the percentage of common variance between the two sets of scores. (1) 3.5 If the slope is 0,13, calculate the intercept. (3) 3.6 Calculate the depression/anxiety score if the students’ physical activity score is 10. (3) 3.7 Give a graphical representation of the regression line by indicating the intercept and the predicted value (calculated above) on this regression line. (5) QUESTION 4 [9] Given a normally distributed population with a mean (μ) of 32, a standard deviation (σ) of 9 and 250 as the number of cases (N), answer the following questions: 4.1 What is the proportion of cases with a raw score less than 25? (3) 4.2 What is the percentage of cases with a raw score greater than 40? (3) 4.3 What is the number of cases with raw scores between 25 and 40? (3) GRAND TOTAL: [45]