Diploma in Financial Management with Public Finance

Transcription

1 Diploma in Financial Management with Public Finance Cohort: DFM/09/FT Jan Intake Examinations for 2009 Semester II MODULE: STATISTICS FOR FINANCE MODULE CODE: QUAN 1103 Duration: 2 Hours Reading time: 10 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. 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. Page 1 of 5

2 SECTION A: COMPULSORY QUESTION 1: (50 MARKS) PART I Analyse the different methods for collecting data. (8 marks) By giving appropriate examples analyse 3 different types of sampling techniques. (12 marks) PART II The data below shows the number of bad debtors recorded by the Finance department for 12 months: Construct a stem and leaf diagram for the above data Calculate the sample mean and sample standard deviation. (6 marks) (d) Determine the (i) median (ii) mode (iii) lower quartile (iv) upper quartile (v) range (vi) interquartile range Using graph paper, draw a box whisker plot for the above data. Comment on the shape of the distribution. (e) Construct a grouped frequency distribution with classes of width 5 starting from the smallest value. Using graph paper, draw a histogram for the distribution. (6 marks) Page 2 of 5

3 SECTION B: ANSWER ANY TWO QUESTIONS QUESTION 2: (25 MARKS) The following represents data from a survey on the promotion exercise of 70 employees of a department in the ministry of Finance. Promoted Not promoted Male Female 12 x Find the value of x. Find the probability that an employee chosen randomly is a male. Find the probability that an employee selected at random is a male and is promoted. (d) Find the probability that an employee chosen randomly is a female or gets promoted. (e) (i) Given that a female is chosen randomly, find the probability that she is promoted. (ii) Using your answer in (i), apply Bayes formula to calculate the probability that the employee is a female given that the employee is promoted. (f) (i) Explain by giving examples what is meant by independent events. (ii) Does promotion at the ministry depends on gender? Justify your answer. Page 3 of 5

4 QUESTION 3: (25 MARKS) The salaries of finance officers in a ministry are found to follow a normal distribution of mean Rs 15, 000 and standard deviation of Rs 4,000. Calculate the probability that an officer chosen randomly gets a salary. (i) less than or equal to Rs13,500. (ii) greater than Rs17,000. (iii) between Rs 14,000 and Rs 16,500. The salary of senior finance officers are normally distributed with a mean of Rs 25,000. It is known that 30% of the senior finance officers get a salary less than Rs 20,000. Estimate the standard deviation of the salary of senor finance officers. (7 marks) The number of years of working experience in a sample 50 employees from the ministry, were found to have a mean of 15 years with a standard deviation of 8 years. (i) Determine the 95 % confidence interval for the average number of years of experience in the ministry. (6 marks) (ii) Interpret your result in (i). Page 4 of 5

5 QUESTION 4: (25 MARKS) The head of the finance department wants to estimate the relationship between the average number of hours of overtime per week (X) and the impact on the increase of the salary (Y) for the year. The following data was collected from a sample of 6 employees. Number of hours overtime (X) % increase in salary (Y) ( X ) ( Y ) X 23.1 Y 23.6 ( XY) Using graph paper, draw a scatter diagram for the above data. (i) Show that the equation of the estimated least squares regression line of heat output on moisture content is given by Y= X (9 marks) (ii) Explain the significance of the coefficients. (iii) On the same graph as in plot the regression line. Calculate the coefficient of correlation for the above data and comment on the result. ***END OF QUESTION PAPER*** Page 5 of 5