Programme BA (Hons) Communication BSc (Hons) Occupational Safety and Health Management BSc (Hons) Applied Social Science with Specialisation in Sociology, Social Services and Criminology BSc (Hons) Applied Social Science with Specialisation in Divinity BSc (Hons) Tourism and Hospitality Management Cohort BAHC/14B/FT BOSHM/15A/FT BSS/14B/FT BSS_D/13B/PT BTHM/14B/FT Examinations for 2015/2016 Semester I & 2015 Semester II MODULE: BUSINESS STATISTICS MODULE CODE: STAT 1101/B Duration: 2 Hours 15 Minutes 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. Always start a new question on a fresh page. 5. Total Marks: 100 This question paper contains 4 questions and 7 pages. Page 1 of 7
SECTION A: COMPULSORY QUESTION 1: (40 MARKS) (a) A business is contemplating to study the training needs of companies in the insurance sector in the Republic of Mauritius. (iii) Carefully explain which, of a census or a sample survey would be more useful for the above study. List the non-sampling errors that could adversely affect the results of the survey. Discuss briefly what could be done to minimize the nonsampling errors in this survey. Discuss two possible modes of administering a questionnaire for this survey and state, with justifications, which mode you would prefer. (4 + 6 + 6 marks) (b) According to the Non Communicable Diseases (NCD) survey 2009 report, out of 2904 Mauritian male participants aged 25 74 years old, 1568 were of normal weight, 1008 were overweight and the rest were obese. The number of female participants in the sample amounted to 3467 of whom 35.1 % were overweight and 20.5 % were of obese. (iii) Tabulate the above information and include in the table any appropriate secondary statistics. What is the percentage of Mauritians who is obese? Comment on the salient feature of the obesity status of Mauritian male participants relative to Mauritian female participants. (7+1+2 marks) Page 2 of 7
(c) In a traffic survey, a random sample of 52 motorists were asked the distance they drove to work daily. The results of the survey are shown in the table below. Distance (km) No. of motorists 0 but under 10 9 10 but under 20 19 20 but under 30 15 30 but under 40 5 40 but under 50 4 Draw a histogram to illustrate this information. Hence, construct a frequency polygon and interpret the diagram obtained. (4 + 5 marks) (d) A cumulative frequency distribution on days absent during a calendar year by employees of a manufacturing company is shown below. Days Absent Cumulative Number of Employees 0-2 60 3 5 31 6 8 14 9 11 6 12-14 2 How many employees were absent between 3 and 5 days? How many employees were absent fewer than six days? (2+3 marks) Page 3 of 7
SECTION B: ANSWER ANY TWO QUESTIONS QUESTION 2: (30 MARKS) For a study on self-awareness, the observed values for one of the groups were as follows: awareness score frequency 0-50 2 51-100 3 101-150 10 151-200 15 201-250 12 251-300 11 (a) (b) (c) (d) (e) (f) (g) Construct an Ogive to represent the data. From your graph, obtain the median. Obtain the interquartile range from the graph. Calculate the mean and comment on the shape of the distribution by comparing with the median calculated above Calculate the variance and give the main disadvantage of such a measure of dispersion. How do nominal variables distinguish from ordinal ones? Distinguish between the qualitative and quantitative approach to data collection, giving examples of each. (5+3+3+4+5+5+5 marks) Page 4 of 7
QUESTION 3: (30 MARKS) (a) Ned has invested in two stocks, Sansa Oil and Arya Mining. Ned has determined that the possible outcomes of these investments three months from now are as follows: Investment Gain or Loss in 3 months (Rs) Sansa Oil Arya Mining 10 000 8 000 5000-2 000 0-20 000 An investment analyst made the following probability assignments for the possible outcomes: Sansa Oil Arya Mining Probability (Rs) (Rs) 10 000 8 000 0.20 10 000-2 000 0.08 5 000 8 000 0.16 5 000-2 000 0.26 0 8 000 0.10 0-2 000 0.12-20 000 8 000 0.02-20 000-2 000 0.06 Calculate the probability that There is a gain There is a gain of Rs 3,000 (iii) There is a loss of Rs 5,000 (iv) Sansa Oil is profitable or Arya Mining is profitable (v) Sansa Oil is profitable and Arya Mining is profitable (5 x 2 marks) (vi) Find the probability that Arya Mining is profitable given that Sansa Oil is profitable. (5 marks) Page 5 of 7
(b) A call center hires part time employees to sell products over the phone. 70% of the employees resign in their first two weeks of employment. The call center hires 6 part time employees. Find the following probabilities: That none of the 6 employees will resign in the first two weeks That at least two of the six employees will resign in the first two weeks. (5+10 marks) QUESTION 4: (30 MARKS) (a) If the p.d.f of a continuous random variable X is given by = where k is a suitable constant, calculate the following: The value of k The probability X lies between 1 and 3 (iii) The variance of X (3+2+5) marks (b) The R & D funds (X in thousands of Euros) of a multinational company is a normally distributed variable. A random sample of 35 subsidiaries belonging to the corporation is selected and it was found out that =20956.15 Find the unbiased estimator for the population mean and standard deviation Obtain a 90% confidence interval for the expected R & D funds. Interpret your answer. (iii) Out of 35 subsidiaries, only 65.71% have public funded R & D projects. Obtain a 95% confidence interval for the proportion of public funded R & D projects (3 5 marks) Page 6 of 7
(c) The weights in grams of oranges grown in a certain area are normally distributed with a mean 227.1 and variance of 265.Estimate the sample size that would be required in order for a 97% confidence interval for to have a width of 8. (5 marks) ***END OF QUESTION PAPER*** Page 7 of 7