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MS-8   june, 2007

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1.Distinguish between decision making under certainty and decision making under uncertainty. Mention certain methods for solving decision problems under uncertainty. Discuss how these methods can be applied to solve decision problems.

2. Use Cramer's rule for a 3 x 3 system of linear equations to solve the following system :

2x - y + 3z =3

-x-y+3z= -6

x-2y-z= -2

3. From the data given below, compute the quartile deviation

4. The members of a Consulting firm rent cars from three rental agencies : 60% from agency l , 30% from agency 2 and 10% from agency 3. if   9% of the cars from agency 1 need a tune-up 20%. of the cars from agency 2 need a tune-up and 6% of the cars from agency 3 need a tune-up, what is the probability that a rental car delivered to the firm will need a tune-up ?

5. To see whether silicon chip sales are independent of where the US economy is in the business cycle, data have been calculated on the weekly sales of a firm and on whether the US economy was rising to a cycle peak, at a cycle peak, falling to a cycle peak or at a cycle trough. The results are

State the null hypothesis. At 0.10 significance level, what is your conclusion ?

(Given the tabulated value of test statistic is 10.645)

6. Write short notes on any three of the following :

(a) Concept of Maxima and Minima

(b) Types of classification of data

(c) Pascal Distribution

(d) Multi-stage sampling & Multi-phase sampling

(e) Box-Jenkins Models for Time Series

7. In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the Delhi half-marathon and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two-week period. What would be the null hypothesis ? Find

a 9o% confidence interval for the percentage of Delhi half-marathon runners who got sick in the two-weeks after the race.

8. A study by a roadways company on the effect of bus-ticket prices on the number of passengers produced the following results :

Develop the estimating equation that best describes the data. Predict the number of passengers per 100 miles if the ticket were Rs. 10.

MS-8   june, 2008

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. What factors       in modern society contribute to  the increasing importance of quantitative approach to  management ? List one applicaticn of quantitative techniques in each functional area of  management.

2. The demand for a certain product is represented by the equation p : 20 + 5q

-q2 where q is the number of units demanded and p is the price per unit. Find marginal revenue function. What is the marginal revenue at q = 2 ?

3 From the frequency distribution, find the standard deviation using the formula fcr the grouped data :

4. A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is ruste,C or a bolt ?

5. In a study to test whether there is a difference between the average height of adult females born in two different countries, random samples yielded the following results :

n1= 120 , mean of x1= 62.7 , and s1=2.5

n2= 150 , mean of x2= 61.8 , and s2=2.62

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

6. Write short notes on any threeof the following :

(a) Step functions

(b) significance of Measures of Dispersion

(c) Criteria of Optimism

(di The F disiribution

e)Auto-regressive (AR) models

7. Given below are figures of production (in thousand kilos) for a sugar factory. Obtain the secular trend by fitting a straight line.

8.Find the area under the standard normal curve, which lies

(a) to the left of z= 0.94

(b) to the right of z= 0.65

(c) to the right of z =1.76

(d) between z =0.34 and z =0.62

MS-8   june, 2009

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

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

2. Which firm, A or B pays out the larger amount as hourly wages ? In which firm A or B, is there greater variability in individual wages ? Bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is d.rawn

at random from one of the bags and is found to be red. Find the probability that it was drawn from bag A.

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

4. A course in Quantitative Applications is taught to 12 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 sfudents 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) :

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 densify tunction (pdf)

(u) Significance level

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

8. Solve the following system of linear equations using matrices :

2x+3y+3z=5

x-2y+z= -4

3x-y-2z= 3

MS-8   june, 2010

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. A car is purchased for Rs. 300,000. If the depreciation for the first three years is at 10% per annum and for the next two years is at 20% per annum, then calculate the

depreciated value of the car at the end of five years.

2. Units A, B, C of a factory manufacture 25%, 35%, 40% respectively of the total cars.

Out of their output, 5%, 4%, 2% defective cars came from the units A, B, C respectively.

Using Baye's Theorem or otherwise, find the probability that a randomly selected car

found defective has come from the unit A.

3.Explain the term Random variable associated with an Experiment. Thereafter distinguish between discrete and continuous probability distributions also mentioning two discrete and two continuous distributions.

4. Compute the Quartile Q3, Decile D5, Percentile P50 and interpret these values in lines 1— 3 for the grouped data showing profits of 100 companies in a year in the table given below :

5. The breaking strength X of cables in a factory has a normal distribution with a mean of p.=1800 lbs and a standard deviation of v = 100 lbs. It is claimed that the breaking

strength X can be increased by the introduction of a new technique in the manufacturing

process. Should we accept the claim on the basis of a sample of 50 cables manufactured

under the new technique; at a significance level of a = .05 given that the mean breaking

strength for the sample is mean = 1850 with the standard deviation remaining the same.

(For convenience, we are giving the result P (Z <=1.645) = .95 where Z has the standard

normal distribution N (0,1)).

6. Write short notes on any three of the following topics :

a) Primary and secondary data

b) Arithmetic Mean and Median of data

c) Sample space associated with an experiment

d) Linear function

(e) Sampling with and without replacement explaining them, mentioning their scope, drawing graphs and giving examples wherever possible.

7. Using the method of least squares, find the regression equation of y on x for the data   given in the Table below :

And from the regression equation obtained, find the value of y corresponding to x = 2.5.

8. Solve the system of non-homogeneous linear equations :

x1 +x2 +2 x3= 2

3x1 — x2+ x3 = 6

-x1+ 3 x2 +4x3=4

by any one method out of cramar's rule, Inverse Matrix method, Gauss-Jordan method.

MS-8   june, 2011

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. You are given the frequency distribution of 292       workers of a factory according to their average weekly income. Calculate quartile deviation and its coefficient from the following data :

2. The Herr- McFee Company, which produces nuclear fuel rods, must X-ray and inspect each rod before shipping. Karen Wood, an inspector, has noted that for every, 1,000 fuel rods she inspects, 10 have interior flaws, 8 have casing flaws, and 5 have both flaws. In her quarterly report, Karen must include the probability of flaws in fuel rods. What is the probability ?

3. The manager of a small postal substation is trying to quantify the variation in the weekly demand for mailing tubes. She has decided to assume that this demand is normally distributed. She knows that on average 100 tubes are purchased weekly and that 90 percent of the time, weekly demand is below 115. What is the standard deviation of this distribution ?

4. The mean length of life of a certain cutting tool is 41.5 hours with a standard deviation of 2.5 hours. What is the probability that a simple random sample of size 50 drawn from this population will have a mean between 40.5 hours and 42 hours ?

5. Before an increase in excise duty on tea, 400 people out of a sample of 500 people were found to be tea drinkers. After an increase in duty, 400 people were tea drinkers in a sample of 600 people. State, whether there is a significant decrease in the consumption of tea. You may use a 5% level of significance.

6. Write short notes on any three of the following

(a) Central Limit Theorem

(b) Stratified Sampling

(c) Less than type Ogive

(d) Level of significance

(e) Coefficient of variation

7. Below are given the figures of production (in m. tonnes) of a sugar factory :

Estimate a linear trend equation and use it to forecast the production for 2009

8. The demand equation faced by DuMont Electronics for its personal computers is given by

P= 10,000 — 4Q, where P= price per unit and

Q= quantity demanded.

(a) Write the marginal revenue equation.

(b) At what price and quantity will marginal revenue be zero ?

(c) At what price and quantity will total revenue be maximized ?

(d) Find the price elasticity of demand at P = 6,000.

MS-8   Dec, 2007

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. Distinguish between decision making under certainty and decision making under uncertainty. Mention certain methods for solving decision problems under uncertainty. Discuss how these methods can be applied to solve decision problems.

2. Use Cramer's rule for a 3 x 3 system of linear equations to solve the following system :

2x - y + 3z = -3

-x-y+3z= -6

x-2y-z= -2

3. From the data given below, compute the quartile deviation.

4. the members of a consulting firm rent cars from three rental agencies : 60% from agency l, 30% from agency 2 and 10% from agency 3. if   9% of the cars from agency 1 need a tune-up , 20%. of the cars from agency 2 need a tune-up and 6% of the cars from agency 3 need a tune-up, what is the probability that a rental car delivered to the firm will need a tune-up ?

5. To see whether silicon chip sales are independent of where the US economy is in the business cycle, data have been calculated on the weekly sales of a firm and on whether the US economy was rising to a cycle peak, at a cycle peak, falling to a cycle peak or at a cycle trough. The results are

6. Write short notes on any three of the following :

(a) Concept of Maxima and Minima

(b) Types of classification of data

(c) Pascal Distribution

(d) Multi-stage sampling & Multi-phase sampling

(e) Box-Jenkins Models for Time Series

7. In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the Delhi half-marathon and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two-week period. What would be the null hypothesis ? Find a 9o% confidence interval for the percentage of Delhi half-marathon runners who got sick in the two-weeks after the race.

8. A study by a roadways company on the effect of bus-ticket prices on the number of passengers produced the following results :

Develop the estimating equation that best describes the data. Predict the number of passengers per 100 miles if the ticket were Rs.10.

MS-8   Dec, 2008

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

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 of Rs. 400 per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of Re.1one 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:

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 :

On the basis of this data, can it be concluded that the model appeal is independent of the age-groups ?

(Given v = 3, and chi square at 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) Minimax criterion of decision making

(e) Standard deviation and standard error

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

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

MS-8   Dec, 2009

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

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

Find the quartile deviation.

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

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 born in two different countries, random samples yielded the following results.

n1=120 , n2 = 150 , mean of x1=62.7 , mean of x2=61.8 and s1=2.50 and 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 at Kolkata from the following data.

Average Price in Kolkata Rs. 65

Average Price in Mumbai Rs. 67

Standard Deviation of prices in Kolkata Rs. 2.5

Standard Deviation of prices in Mumbai Rs. 3.5

Correlation coefficient between two + 0.8 prices 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 a continuous random variable.

(e) Power curve of a test.

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 inoney the tour operator receives.

MS-8   Dec, 2010

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

MS-8   Dec, 2011

MS-8 : QUANTITATIVE ANALYSIS FOR MANAGERIAL APPLICATIONS

1. What do you understand by a continuous frequency distribution ? Explain various terms that are frequently used in a frequency distribution. Also highlight the difference in inclusive and exclusive methods of classes.

2. Consider the following matrix of transition

probabilities of a product available in the market

in two brands.

                               Brand A                                      Brand B

Brand A                  0.9                                                0.1

Brand B                   0.3                                                 0.7

Determine the market shares of each of the brand in equillibrium position

3. A manufacturer buys parts from four different vendors numbered 1, 2, 3, and 4. Referring to orders placed on two successive days, (1, 4) denotes the event that on the first day, the order was given to vendor 1 and on the second day it was given to vendor 4. Letting A represent the event that vendor 1 gets at least one of these two orders, B the event that the same vendor gets both orders and C the event that vendors 1 & 3 do not

get either order. List the elements of (a) Entire sample space (b) BUC (c) A

4. In a random sample of 500 people of a city, it was found that 160 people have a car from Maruti Suzuki family. Find a 95% confidence interval for the actual proportion of people who have a car from Maruti Suzuki family.

5. Quotations of index numbers of equity shares price of a certain joint stock company and of prices of preference shares are given below :

Use the method of Rank correlation to determine the relationship between equity share and preference share prices.

6. Write short notes on any three of the following :

(a) Inductive statistics

(b) Skewness

(c) Criterion of pessimism

(d) Double sampling

(e) Auto - correlation & Time series

7. The incomes of a group of 10,000 people were found to be normally distributed with mean Rs 7500 p.m and standard deviation Rs 500. Show that of this group 95% had incomes exceeding Rs 6680 and only 5% had income exceeding Rs 8320.

8. The following table gives the number of accounting clerks committing errors and not

committing errors between trained and untrained clerks working in an organisation :

Test the effectiveness of training in preventing errors. Use 0.05 level of significance

Given X at 1 d.f and a=0.05 =3.841).