Question 1 A manufacturing company has three processing lines. Each processing line combines various raw materials to produce the same output. One of the processing lines can combine units of input to produce units of output such that there is a linear relationship between input and output. The Chief Executive Ofcer wants the output model to be estimated for this processing line. Given the values of input and output (in thousands of units) in the table below, and as the Director of Data Management, you are to: Input 5 7 2 8 4 output 8 12 6 l4 8 a) Determine the extent to which output changes as the input change and interpret your result. (3 marks) b) Find the intercept of the output model and interpret it. Write down the equation of the line of best t for output. (3 marks) c) Determine the value of the extent of relationship between the input and output, and interpret your result. (3 marks) (1) Find the value of the coefcient of determination and interpret your result. (3 marks) e) What will be the output level if the input usage is 15? (1 mark) f) What percentage of the changes in output is due to other raw materials? (2 marks) g) Test at 1 percent signicance level, whether the correlation between input and output exist. (5 marks) Question 2 Students are usually tested on various subjects to determine their level of intelligence. In an intelligence examination administered to 2,000 students of the MBA programmes, the average score recorded by the Lecturer was 42 and deviation of the scores from their mean was 24. Assuming that the distribution of scores is normal, nd: i. The number of students whose score exceeds 50. (4 marks) ii. The number of students whose score is between 30 and 54 inclusive. (4 marks) iii. The score corresponding to the standardized normal value of 2. (4 marks) iv. What is the probability of a score which is less than '70? (4 marks) v. How many student would have a score of at least 66? (4 marks) Page 2 of 13 Question 3 Question 3(a) Ekuba is the Receptionist for Tootooba Company Limited. Among her duties, she is to receive external phone calls to the company. She has one hour for lunch break, usually between the hours of 12:00 noon and 1:00 pm, per day. On a typical working day, the average number of phone calls per hour received on the phone switchboard of the company is 3. Based on this information, nd the probability that, during one particular break hour: i) From 3 to 4 phone calls inclusive were registered on the phone switchboard. (4 marks) ii) At least two call were registered on the phone switchboard. (4 marks) iii) More than three calls were registered on the phone switchboard. (4 marks) [Round values to three decimal places] Question 30)) It is known that, applicants for a new graduate MBA programme in UPSA School of Graduate Studies either get admitted or not. In the School of Graduate Studies, an admission rate of 70% has been reported. If 10 applicants are selected at random, nd the probability that: i) More than 8 applicants will be admitted. (4 marks) ii) Fewer than 8 applicants will be admitted. (4 marks) [Round values to three decimal places] Question 4 Question 4(a) Assume the waiting time to buy 'streetwise' pack of KFC at the Agboba Junction is normally distributed. Two senior staff members of UPSA, Kobina and Yaw, who are customers of KFC were informed of their standardised waiting time as 0.75 and 0.5 respectively. On one Sunday evening, they went to buy a 'streetwise' pack. Suppose the waiting time of these two senior members are 32 and 24 minutes respectively, nd the mean and standard deviation of the waiting time of all customers buying 'streetwise' pack from that KP C shop on that Sunday. (7 marks) Question 4(b) Key characteristics of real life events in which the outcomes are dichotomous in nature are the probabilities of occurrence and non-occurrence. The information on one such event is that 'the mean of a particular job application binomial Page 3 of [3 distribution is 15 and its standard deviation is 3 '. To dene the boundaries of the distribution, nd the values of a , the probability of success, 1}: the probability of failure and n, the sample size. Is there any inconsistency in the statement? ('7 marks) Question 4c The table below shows the numbers of public and private special schools both here in Ghana and the rest of Africa (ROA). Public Private Ghana ROgA Ghana RQIA 14 Fine Arts 10 641;) General Arts 15 13 12 If a school is chosen at random, nd the probability that, it is i. Private or in the rest of Aica (3 marks) ii. A science school or Ghana (3 marks) Question 5 Investment products have different probabilities of success. A businessman wishes to invest in two different products, A and B. The following table shows the probability distributions, where P(a, b) represents the probability of success of the i\" investment of A and the i\"ll investment of B, for the values (in thousands of GH) for A and B invested in 4 different years. Base on this information: (3) Which of the investments has a better return and why? (4 marks) (b) Which of the investments is relatively less risky and why? (4 marks) (c) What type of association exists between the two investment options A and B? Interpret your results. (4 marks) (d) One bag contains 5 green and 3 blue balls. Another bag contains 4 green and 2 blue balls. If one ball is drawn from each bag, nd the probability that one is green and the other is blue (4 marks) Page 4 of 13 Question 6 Question 63 The performance of students is determined by several factors. These factors relate to the students' characteristics, learning environment and the external peculiar conditions. For a sample of 27 students selected from a post-graduate programme in UPSA, the estimated students' performance model results are presented in the tables below. M 099198 S-uare 3.04162 27 __-_ ----- F _-l Error value 95% 95% rm -- _--_ 0392433 m-\"u 1.467680 swimming 1.654349 - 0.159969 Page 5 of 13 i. Write down the estimated model. (2 marks) ii. Which of the variables are statistically signicant? (2 marks) iii. If the value of IQ changes by a unit, what range of values can students' performance take? (2 marks) iv. What is the contribution of the ve factors to the changes in performance of students? (2 marks) v. Is the overall performance model statistically signicant? Prove. (2 marks) Question 6b Customers have two choices, either to go to Marina Mall or Koala Mall during the Christmas holidays. The total expenditure recorded on the Farmers\" Day (in thousands of GH) are presented in grouped data equency distribution table below for the two malls. By assumption, the malls have the same expected average expenditure for the Christmas holidays. Base on this information, which mall can be relatively sure of achieving the mean expenditure by customers? (10 marks)