Term-End ExaminationJune, 2009

MS-8: QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

SECTTON . A

1.An analysis of the hourly wages paid to workers in two firms A and B belonging to the sameindustry gives the following results:

Firm A Firm BNumber of wage-earners 586 648Average hourly wage Rs.52.5 Rs.47.5Variance of the distribution of wage

100 121

(a)Which firm, A or B pays out the larger amount as hourly wages?(b)In which firm A or B, is there greater variability in individual wages?

2. Bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag A.

conditional probability problem.

P[bag A & red] = [1/2][3/5] = 3/10 = 27/90P[bag B & red] = [1/2][5/9] = 5/18 = 25/90P[red] = sum of the above = 52/90

P[bag A | red] = P[bag A & red] / P[red]= 27/52

3. What do you understand by probability sampling ? Describe stratified and cluster samplingDesigns. What is the difference between a cluster and a strata ?

4. A course in Quantitative Applications is taught to L2 students by conventional classroom procedure. A second group of 10 students was given the same course by programmed materials. The same examination was given to each Soup at the end of the course. The 12 classroom students scored 85 marks on an average with the standard deviation 4, while 10 students using programmed material scored SL marks on an average with a standard deviation of 5. Test whether the two methods of learning are equally effective? Use 0.10 level of significance.

5. The information given below relates to the advertisement and sales of a company(in lakhs of Rupee )

Advertisement Expenditure (X)

Sales (Y)

Arithmetic Mean 20 100

Standard Deviation 3 12

Correlation coefficient between X & Y = 0.8

(a) Find the two regression equations.(b) What should be the advertisement expenditure if the company wants to attain sales target of Rs 120 lakhs ?

6.Write short notes on any three of the following :(a) Marginal Revenue(b) Exponential Smoothing(c) Less than type Ogive(d) Probability density Function (pdf)(e) Significance level

SECTTON – B

7. In a random sample of 500 people of a city, it was found that 160 preferred seafood. Find a 95% confidence interval for the actual proportion of people who preferred seafood.

p-hat = 160/500 = 0.32

---ME = 1.96*sqrt(0.32*0.68/500) = 0.0410----95% CI: 0.32-0.0410 < p < 0.32+0.0410

8. Solve the following system of linear equations using matrices

2 x + 3 y + 3 Z = 5x - 2y + z = - 43 x - y - 2 z = 3

Term-End ExaminationDecember, 2009

MS-8: QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

SECTTON . A

1.The following data describes the age at which employees reach to the level of 'senior manager'in a multinational company

Age in years Below 34.5

34.5-37.5 37.5-40.5 40.5-43.5 Over 43.5

No of peoplereaching the level

14 60 95 24 7

Find the quartile deviation

2. In a bolt factory, machines A, B, C manufacture respectively 25%, 35% and 40% of the totalproduction. Of their output 5%, 4% and 2% respectively are defective bolts. A bolt is drawnat random and is found to be defective. What is the probability that it is manufactured bymachine B ?

Solution :

Let E be the probability of drawing defective bolt. Let E1, E2 and E3 be the event of drawing a bolt produced by the Machines A, B and C respectively. Then P(E1) = 25/100, P(E2) = 35/100, P(E3) = 40/100, P(E/E1) = 5/100, P(E/E2) = 4/100, P(E/E3) = 2/100. Therefore, P(E2/E) = [P(E2).P(E/E2)]/[P(E1).P(E/E1) + P(E2).P(E/E2) + P(E3).P(E/E3)]

= [(35/100)(4/100)]/[(25/100)(5/100) + (35/100)(4/100) + (40/100)(2/100)] = [35×4]/[25×5 + 35×4 + 40×2] = 140/(125 + 140 + 80) = 140/345 = 28/69.[Ans.]

3.Describe the design of stratified sampling. What is a strata ? Discuss about proportional allocation and disproportional allocation.

4. In a study to test whether there is difference between the average heights of adult females bornin two different countries, random samples yielded the following results.

n1 = 120 x1= 62.7 s1= 2.50

n2 =150 x2 = 61.8 s2 = 2.62

where the measurements are in inches. Use 0.05 level of significance to test the difference between the average heights.

5.Find the most likely price of commodity A in Mumbai corresponding to the price of Rs. 70 atKolkata from the following data

Average Price in Kolkata Rs. 65Average Price in Mumbai Rs. 67Standard Deviation of prices in Kolkata Rs. 2.5Standard Deviation of prices in Mumbai Rs. 3.5Correlation coefficient between two + 0.8prices in two towns

6.Write short notes on any three of the following :a)Cramer's Rule.b)Exponential Smoothing.c)More than type ogive.d)Cumulative Density Function (cdf) of ae)continuous random variable.(f )Power curve of a test.

SECTION-B

7.In a locality containing 18000 families a sample of 840 families was selected at random. Of these 840 families 206 families were found to have a weekly income of Rs. 500 or less. It is desired to know how many out of 18000 families have a weekly income of Rs. 500 or less. Use 3 sigma limits.

8.A tour operator charges Rs. 136 per passenger for 100 passengers with a discount of Rs. 4 for every group of 10 passengers in excess of 100. Determine the number of passengers that will maximize the amount of money the tour operator receives.

December, 2OO8

SECTION A

l. Explain Hypothesis testing. What are the steps involved in hypothesis testing ? Discuss the two types of errors in testing of hypothesis.

2.A telephone company in a town has 1000 subscribers on its list and collects a fixed charge ofRs. 400 per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of Re. 1, one subscriber will discontinue the service. Find what increase will bring maximum revenue to the company.

3.A husband and wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 1/7 and that of wife's selection is l/5. What is the probability that

(a) both of them will be selected ?(b) only one of them will be selected ?(c) none of them will be selected?(d) at least one'of them will be selected ?

4. To test the effectiveness of training, a group of 5 participants were selected and given a test before and after the training. The result of the tests was as under:

Participant 1 2 3 4 5

Score before training

10 12 15 18 10

Score after training 15 10 18 32 25

Can the training be regarded as effective at 5 percent level of significance?

5. An automobile company gives you the following information about age-groups and the liking for a particular model of car which is expected to be introduced :

Age

Persons ≤ 20 20 - 39 40- 59 ≥ 60 Total

Liked the car 140 80 40 20 280

Disliked the car 60 50 30 80 220

Total 200 130 70 100 500

On the basis of this data, can it be concluded that the model appeal is independent of the age-groups? (Given v = 3, Chi-square (0.05) = 7.815)

6. Write short notes on any three of the following :(a) Minor of an element of matrix(b) Equally likely events(c) Advantages of probability sampling(d) Mini max criterion of decision making(e) Standard deviation and standard error

SECTION B7. Obtain the two regression equations for the following data using the method of least squares.

x 1 2 3 4 5y 5 7 9 10 11

8. Determine the sample size if sample standard deviation s = 6, population mean = 25,Sample mean = 23 and the degree of precision is 99%.