IOP2601 Assignment 2 (DETAILED ANSWERS) Semester 2 2024 - DISTINCTION GUARANTEED

IOP2601 Assignment 2 (DETAILED ANSWERS) Semester 2 2024 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references .. QUESTION 1 [11] Use the information below to answer the questions that follow. A local community centre will soon be celebrating its annual "Volunteer of the Year" award, with the winner receiving a R20 000 gift card and a certificate of appreciation. Two volunteers, Sonia and Jack, are finalists for this prize. Sonia has been volunteering at the centre for fifteen (15) years and is recognised for her dedication and vast contributions. She received 40 nominations from various community members. Jack is a new volunteer who has made a big impact with his energy and innovative ideas. He received 20 nominations from both community members and employees. The community centre's administration received 200 valid nominations. Sonia and Jack are now excitedly anticipating the announcement of the winner, conscious that their chances are determined by the number of nominations they received, as well as the selection committee's considerations. 1.1 What is the probability that Sonia will win first prize? (2) 1.2 What is the possibility that Jack will win first prize? (2) 1.3 If Sonia wins first prize, what is the probability that Jack will win second prize? (The person winning the first prize is not eligible to be selected for the second or third prize). (2) 1.4 If Jack wins the first prize, what is the probability that Sonia will win the second prize? (The person winning the first prize is not eligible to be selected for the second or third prize). (2) 1.5 What is the probability that Sonia and Jack will win first and second prize, respectively? (3) 2 IOP2601/Assessment 2/SEM2/2024 [TURN OVER] QUESTION 2 [23] A Nigerian researcher conducted a study on the impact of study group participation on the academic performance of first-year university students. The researcher found that students who regularly participated in study groups had higher academic achievements than those who studied alone or only attended lectures. A researcher at the University of South Africa (Unisa) aimed to assess the relevance of the Nigerian researcher’s findings within the South African educational context. To do so, the Unisa researcher began by analysing the correlation between participation in study groups (X) and academic achievement (Y). The findings were as follows: N = 10 ƩX = 33 ƩX2 = 125 ƩY = 32 ƩY2 = 112 ƩXY = 114 ƩXƩY = 33 x 32 = 1056 (ƩX)2 = (33)2 = 1089 (ƩY)2 = (32)2 = 1024 2.1 Calculate the relationship between utilising the university library and academic achievement scores. (3) 2.2 Interpret the correlation coefficient. (2) 2.3 What can you deduce from the nature of the relationship between utilising the university library and academic achievement? (1) 2.4 Calculate the percentage of common variance between the two sets of scores and illustrate it in a diagram. (3) 2.5 Calculate the slope. (3) 2.6 Calculate the intercept. (3) 2.7 Calculate the academic achievement score if the study group participation score is 7. (3) 2.8 Give a graphical representation of the regression line by indicating the intercept and the predicted value (calculated above) on this regression line. (5) 3 IOP2601/Assessment 2/SEM2/2024 [TURN OVER] QUESTION 3 [9] Given a normally distributed population with a mean (μ) of 10, a standard deviation (σ) of 2, and 50 as the number of students (N), answer the following questions: 3.1 What is the proportion of students with a raw score greater than 12? (3) 3.2 What is the percentage of students with a raw score less than 6? (3) 3.3 What is the number of students with raw scores between 6 and 12? (3) QUESTION 4 [7] Answer the following questions. (1 mark each) 4.1 What does the direction of the correlation indicate? 4.2 How is the strength of a correlation determined? 4.3 On a scatter diagram, how is a linear relationship between two variables presented? 4.4 When interpreting correlation coefficients, which of the following terms should be avoided? A. relationship B. association C. cause D. correlation 4.5 Which of the following is a correct interpretation of a correlation coefficient of r = 0.90? A. High scores on one variable cause high scores on the other. B. There is a strong association between high scores on both variables. C. The correlation indicates a 90% relationship between the two variables. D. One variable influences the other. 4.6 What term is used to describe a relationship that does not form a straight line on a scatter diagram? A. linear relation B. nonlinear relation C. direct correlation D. inverse correlation 4 IOP2601/Assessment 2/SEM2/2024 4.7 What does a linear relationship between two variables imply? A. The variables are independent of each other. B. The relationship can be represented as a straight line on a scatter diagram. C. There is a cause-and-effect relationship between the variables. D. The correlation coefficient is always positive.