IOP2601 Assignment 2 (ANSWERS) Semester 1 2024 - DISTINCTION GUARANTEED.

Well-structured IOP2601 Assignment 2 (ANSWERS) Semester 1 2024 - DISTINCTION GUARANTEED. (DETAILED ANSWERS - DISTINCTION GUARANTEED!). . (DETAILED ANSWERS - DISTINCTION GUARANTEED!). .... QUESTION 1 [11] Use the information below to answer the questions that follow. “Employee of the Month” Selection A large corporation presents an annual "Employee of the Month" award, where the winner receives a bonus of R10 000 along with recognition and a certificate of appreciation. Two employees, Zodwa and MacGyver, are competing for this prestigious title. Zodwa has been with the company for five (5) years and is known for her exceptional performance and dedication. She received 50 nominations, highlighting her achievements and contributions to various projects. MacGyver, on the other hand, is a relatively new employee but has quickly made an impact with his innovative ideas and teamwork. He received 30 nominations, from colleagues and supervisors. After the nomination process, the HR Department announces that they received a total of 200 valid nominations, and Zodwa and MacGyver have both qualified for consideration. Now, Zodwa and MacGyver are anxiously awaiting the announcement of the winner, knowing that their chances are influenced not only by their own efforts but also by the overall pool of nominations and the judgement of the selection committee. 1.1 What is the probability that Zodwa will win first prize (2) 1.2 What is the possibility that MacGyver will win first prize? (2) 1.3 If Zodwa wins first prize, what is the probability that MacGyver 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 MacGyver wins the first prize, what is the probability that Zodwa 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 Zodwa and MacGyver will win first and second prize, respectively? (3) 2 IOP2601/S1/2024/Assessment 2 [TURN OVER] QUESTION 2 [23] An American professor conducted a study on the influence of the learning environment on the academic achievement of second-year university students. The results of his research indicated that students who studied mostly at the university library achieved higher academic performance when compared to those who favoured studying in their dormitory rooms or in off-campus housing. A researcher at Unisa sought to evaluate the validity of the professor's research in the South African context. The researcher began by examining the correlation between utilising the university library (X) and academic achievement (Y). The findings are as follows: N = 10 ƩX = 30 ƩX2 =100 ƩY = 35 ƩY2 = 133 ƩXY = 110 ƩXƩY = 30 x 35 = 1050 (ƩX)2 = (30)2 = 900 (ƩY)2 = (35)2 = 1225 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 about 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 utilising the library score is 10. (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) QUESTION 3 [9] Given a normally distributed population with a mean (μ) of 6, a standard deviation (σ) of 2, and 40 as the number of cases (N), answer the following questions: 3.1 What is the proportion of participants with a raw score greater than 4? (3) 3.2 What is the percentage of participants with a raw score greater than 10? (3) 3.3 What is the number of participants with raw scores between 4 and 10? (3) 3 IOP2601/S1/2024/Assessment 2 RN OVER] QUESTION 4 [7] 4.1 What are the fundamental differences between descriptive and inferential statistics?(4) 4.2 Explain the characteristics of a normal distribution. (3)