Programme BSc (Hons) Accounting with Finance BSc (Hons) Banking and International Finance BSc (Hons) Financial Services with Law BSc (Hons) Human Resource Management BSc (Hons) Logistic and Transport Management BSc (Hons)/Diploma Human Resource Management BSc (Hons) Management (G+F+L+M) COHORT BACF/13B/14A/15A/16A17A/FT/ PT BBIF/12B/14B/17A/FT B1 BFSL/13B/FT BHRM/12B/13B/14B/15B/16B/17 A/FT/PT BLTM/13B/FT BHRM/DHRM/17A/FT BMAN/G/M/L/F/13A/13B/14A/14B /15B/16A/16B/17A/FT/PT B1 & B2 Examinations for Academic Year 2016 2017 Semester II / Academic Year 2017 Semester I MODULE: STATISTICS MODULE CODE: QUAN 1102 DURATION: 2 HOURS Instructions to Candidates: 1. This question paper consists of Section A and Section B. 2. Section A is compulsory. 3. Answer any two questions from Section B. 4. Non programmable calculators are allowed but relevant workings must be clearly shown. 5. Always start a new question on a fresh page. 6. Total Marks: 100. This Question Paper contains 4 questions and 5 pages. This Question Paper is printed on BOTH SIDES. Page 1 of 5
QUESTION 1: (40 MARKS) SECTION A: COMPULSORY PART I Explain three types of commonly used sampling techniques. Illustrate each of them with appropriate examples. (9 marks) PART II The data below shows the daily number of applications recorded by a Department of the Ministry over a period of 20 days. 23 42 45 50 30 37 54 56 61 49 65 55 27 32 36 58 62 67 53 56 (a) Using the given data, form a grouped frequency distribution using class width of 9 and number of classes being 5. (b) Using the distribution obtained at (a), evaluate an estimate of the mean, standard deviation, variance and coefficient of variation. (10 marks) (c) (d) Using graph paper, draw a histogram to represent the frequency distribution of the given data and find an estimate for the mode. Using graph paper, plot a cumulative frequency curve for the frequency distribution and determine the 10 th to 90 th percentile range. (e) Construct a stem-and-leaf display. Hence find the median. (f) Using graph paper, draw a box and whisker diagram to represent these data and comment on the shape of the distribution. Page 2 of 5
SECTION B: ANSWER ANY TWO QUESTIONS QUESTION 2: (30 MARKS) (a) A fruitseller has imported boxes of fruits, namely, apples, oranges and grapes from India and South Africa as follows: Country of Origin Apples Oranges Grapes India 56 81 74 South Africa 121 157 105 1. Determine the probability that a randomly selected box: (i) is from India and contains grapes (1 mark) (ii) contains apples or is from South Africa (2 marks) (iii) is from South Africa given that it contains oranges (2 marks) (iv) contains grapes given that it is from India (2 marks) 2. (i) Using relevant examples, differentiate between the term independent event and mutually exclusive events (ii) Is the content of the box statistically independent of its origin? Justify your answer. (b) The following table depicts the likely harvest of pineapples for four weeks. Harvest of pineapples in Kg 350 400 450 500 Probability 0.30 0.35 0.15 0.20 Calculate the mean and standard deviation of the likely harvest of pineapples for the coming four weeks. (c) 9 students sat for an exam whereby the probability of success is 0.45. (i) Justify which probability distribution can be used to model the above. (ii) Find the probability that at least two students succeeded in the exams. (d) Suppose the number of accidents on a particular highway in an hour has a Poisson random variable with parameter 1.50. Find the probability that more than one accident occurred in four hours. Page 3 of 5
QUESTION 3: (30 MARKS) (a) After extensive testing, it was found that the lifetimes of a certain type of light bulbs had a mean of 2408 hours and a standard deviation of 101 hours. Assuming that the lifetime of these bulbs is modeled by a normal distribution, (i) Find the probability that a light bulb will have a lifetime 1. more than 2600 hours. 2. between 2200 hours and 2500 hours. (ii) Find the value of k given that 95% of such light bulbs have a lifetime of less than k hours. Give your answer to the nearest hour. (iii) Find the probability that the mean lifetime of a random sample of 36 such light bulbs is less than 2450 hours. (6 marks) (b) In a normal distribution, 69% of the distribution is less than 28 while 90% is less than 35. Find the mean μ and standard deviation σ of the distribution. (7 marks) (c) A sample of 200 similar packets of breakfast cereal was examined and the mass of the contents in each packet was noted. The following results were obtained: sample mean = 341.2 g, sample standard deviation = 0.92 g. Calculate a 95% confidence interval for the mean mass of the contents in all packets of this type, stating any assumptions that you make. (6 marks) Page 4 of 5
QUESTION 4: (30 MARKS) (a) What are the assumptions associated with the simple linear regression model? (b) A Private Company in Mauritius administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict their eventual success. The table below records average weekly sales (in thousands of rupees) and aptitude test scores for a random sample of eight representatives. Representatives 1 2 3 4 5 6 7 8 Weekly Sales, x (in thousands, Rs) 10 12 28 24 18 16 15 12 Test Scores, y 55 60 85 75 80 85 65 60 (i) Draw a scatter diagram of the given data on graph paper and comment on the relationship between x and y. (ii) Find the equation of the estimated least squares regression line of y = a + bx and plot the line on the same graph as the scatter diagram. Interpret the values of a and b in your least squares regression line. (14 marks) (iii) Calculate the correlation coefficient and the coefficient of determination. State what this indicate about the relation between x and y. (iv) Estimate the test score for a representative when the weekly sales is: (1) 17,000 (2) 30,000 Comment on the reliability of the estimates. ***END OF QUESTION PAPER*** Page 5 of 5