Calicut University 2006 M.Com Commerce QUANTITATIVE TECHNIQUES - Question Paper

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FIRST SEMESTER M.Com. DEGREE EXAMINATION, NOVEMBER 2006

Paper 1-2QUANTITATIVE TECHNIQUES (2004 admissions)

Time : Three Hours Maximum : 80 Marks

Part A .

Answer all questions.

Each question carries 2 marks.

1. What is meant by discrete random variable ?

r

2. What is a probability distribution ?

3. State law of large numbers.

4. Define expectation of x.

5. What is 2-static ?

(5 x 2 = 10 marks)

Part B

Answer any four questions. ' 0 ...... Each question carries 10 marks. t -

6. (a) State addition theorem of probability.

(b) 20 per cent of the bolts produced in a given machine is on the average found defective. If 10 bolts are selected at random from one days production, find the probability that 3 of them will be defective. p ' \ .

7. (a) A binomial distribution has n = 20 ,p- 0-4. Calculate the mean and variance of the distribution,

(b) Distinguish between One-tail and Two-tail tests. yfcT f) p

8. To ascertain whether the high income families have a tendency to send their children to private schools, a survey was conducted among 2,000 families and the following results were obtained :

No. of children in

___ *

Private School Government School

Low income families ... 400 450

High income families ... 600 550

How do you test these results ?

9. Bring out the relative merits and demerits of stratified random sampling and cluster sampling methods.

Turn over

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10. From the following data on samples; taken from a production process, construct .an X -dhart ami'lO an R-chart. Determine whether the process is under control : \

V

Sample No. 1 2 3 4 5 6 7 8 ₀<

X : 20 34 45 40 25 30 16 30

R 16 28 15 10 17 15 6 12

11.Given the two regression lines, 3y = 2x + 6 and 5x = y + 20, find x and y. Also calculate the standard deviation of y, if the standard deviation of x is 3. ,

(4 x 10 = 40 marks)

Part Cl

Answer any, two questions.

Each question carries 15 marks.

12. What is Analysis ofVarianee Technique ? Explain how this technique is used in business decisions.

13. l)iscuss the properties and uses of Normal distribution in decision-making.

14. Write notes on :

(a) Type I and Type II errors.

(b) Sequential sampling.

(c) Chi-square test.

(2x15 = 30 marks)

f)