MS08 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

DEC 2003

Note :

(i) Section A has six questions, each carrying 15 marks. Attempt any four.

(ii) Section B is compulsory and carries 40 marks. Attempt both questions.

(iii) Statistical tables may be supplied on demand.

SECTION A

1 What is a random variable and its probability distribution? Explain two summary measures of a probability distribution and discuss their possible applications in business. [15]

2 In order to get the best talent in the country and ensure a pay package that is relevant for a long time, a company has formulated a policy for the pay package. Going by the policy, an employee who received fixed annual increments, had a salary of Rs. 90,000 per annum after having worked for 10 years. His total sum of salary received was Rs. 6,50,000 over the period of 10 years. Find out what was his initial salary and annual increment. [15]

3 A researcher is interested in determining the rate of coffee usage per household. He believes that yearly consumption per household is normally distributed with an unknown mean (m) and a standard deviation (s) of 1.25 kg. How large a sample must he take in order to be 98% certain that the sample mean is within 0.5 kg of the population mean (m)? [15]

4 In a regression analysis problem with a sample size of 17, the slope was found to be 3.73 and the standard error of residue is 28.654. The quantity (å X2 - ) = 871.56. [15]

(a) Find the standard error of the regression slope coefficient.

(b) Construct a 98% confidence interval for the population slope.

5 A production manager feels that the output rate of experienced employees is surely greater than that of new employees, but he does not expect the variability in output rates to differ for the two groups. In previous output studies, it has been shown that the average unit output per hour for the employees with five years of experience at this particular type of work is 30 units per hour with a variance of 28 units. For a group of 20 new employees, the average output for the same type of work is 20 units per hour with a sample variance of 56 units. Does the variability in the output of the new group differ from that of the experienced group? Test the hypothesis at 0.05 level of significance (a). [15]

6 Write short notes on any three of the following: [15]

(a) Unit of a function

(b) Bowley’s coefficient of skewness

(c) Normal distribution as an approximation of Binomial distribution

(d) Testing for significance of correlation coefficient (r)

(e) Comparison between mean and median

SECTION B

7 The latest political survey indicates that the probability that voters support party ‘C’ is 0.55, the probability that they support party ‘L’ is 0.30 and the probability that they are ‘Neutral’ is 0.15. Using these probabilities, answer the following questions for 10 randomly selected voters: [20]

(i) What is the probability that 2 voters are ‘neutral’?

(ii) What is the probability that at least 8 voters support party ‘L’?

8 A ketchup manufacturer is in the process of deciding whether to produce a new spicy brand. A telephone survey of 6000 households found that only 335 households would purchase the new brand. A study made 2 years ago for the same brand showed that 5% of the households would purchase this brand. At 2% significance level, should the company conclude that there is an increased interest in the spicy flavour now? [20]