Assignments Program Mbjk..j.a 2yrs Semester-i

ASSIGNMENTSPROGRAM:MBA 2yrs

SEMESTER-I

Subject Name : Quantitative Techniques in Management

Batch :

Permanent Enrollment Number (PEN) :

Roll Number :

Student Name :

INSTRUCTIONS

a) Students are required to submit all three assignment sets.

ASSIGNMENT DETAILS MARKS

Assignment A Five Subjective Questions 10 Assignment B Three Subjective Questions + Case Study 10Assignment C 40 Objective Questions 10

b)  Total weightage given to these assignments is 30%. OR 30 Marks c)  All assignments are to be completed as typed in word/pdf. d) All questions are required to be attempted. e) All the three assignments are to be completed by due dates (specified from time to time) and need to

be submitted for evaluation by Amity University. f) The evaluated assignment marks will be made available within six weeks. Thereafter, these will be

destroyed at the end of each semester. g) The students have to attach a scan signature in the form.

Signature :_________________________________

Date : _________________________________

( √ ) Tick mark in front of the assignments submitted

Assignment ‘A’ Assignment ‘B’ Assignment ‘C’

Assignments - A

Problem 1: From the following data calculate the missing the missing frequency.

No. of Tablets No. of Persons cured

4-8 118-12 13

12-16 1616-20 1420-24 ?24-28 928-32 1732-36 636-40 4

The average number of tablets to cure fever was 19.9.

Solutions 1:

No. of Tablets No. of Persons cured(f)

4-8 118-12 13

12-16 1616-20 1420-24 ?24-28 928-32 1732-36 636-40 4

  90

Mid-point calculation Mid-point (x)MidPoint*person

cured (fx)(4+8) / 2 = 6 66

(8+12) / 2 = 10 130(12+16) / 2 = 14 224(16+20) / 2 = 18 252(20+24) / 2 = 22 x(24+28) / 2 = 26 234(28+32) / 2 = 30 510(32+36) / 2 = 34 204(36+40) / 2 = 38 152

    1772

The average number of tablets to cure fever was 19.9.

X=9, Answer is 9.

Problem 2: You are supplied the following data about heights of students in a college.Boys Girls

Number 72 38Average height (inches) 68 61Variance of distribution 9 4

Find out:(a). In which sex, boys or girls, is there greater variability in individual heights.(b). Common average heights in boys and girls.(c). Standard deviation of height of boys and girls taken together.(d). Combined variability.

Solutions 2: We have following data about heights of students in a college.Boys Girls

Number- 72 – n1 38 – n2

Average height (inches) 68 – x1 61 – x2

Variance of distribution 9 – var1 4 – var2

(a). In which sex, boys or girls, is there greater variability in individual heights. Ans) To find variability, we use formula of coefficient of variance, which is= SD/mean *100so boys have 4.4% n girls have 3.2% variability. So the boys have greater variability in heights.

(b). Common average heights in boys and girls. Ans) To find average height, we use the formula of combined mean, which is = (n1x1+n2x2)/(n1+n2) Combined Mean= (68*72+61*38)/110. Ans. 65.58

(c). Standard deviation of height of boys and girls taken together.Ans) To find above, we use formula of combined SD formula, which is= ( (n1-1)sd1 + (n2-1)sd2) / (n1+n2-2)

1772+22x =19.9

90+x

By putting values in the formula, we get 7.28 => 2.69

(d). Combined variability.Ans) by taking the square of Ans c, we will get combined variability. Which is = 7.28

Problem 3: The sales of a company in thousands of Rs for the year 1965 through 1971 are given below:Year 1965 1966 1967 1968 1969 1970 1971

Sales 32 47 65 92 132 190 275

Estimate the sales figure for the year 1972 using an equation of the form. Y=abx where x= year and Y= sales.

Solution Taking logs: log Y=loga + xlogb

Year x Sales (Y) log Y x^2 x .logY1965 -3 32 1.50515 9 -4.515451966 -2 47 1.672098 4 -3.34421967 -1 65 1.812913 1 -1.81291

-9.672561968 0 92 1.963788 0 0

1969 1 132 2.120574 1 2.1205741970 2 190 2.278754 4 4.5575071971 3 275 2.439333 9 7.317998

13.99608      13.79261 28 4.32352

Substituting the values in the expression

and

We get

and

Thus the equation becomes

log b =∑x.log Y

∑x2

log b =4.3237

=0.15428

log Y =1.9515 + .154x

Origin 1969 Time Unit = 1 year

For 1972x would be +4. Putting this value

logY = 1.9515 + .154(4)

logY = 1.9515 + .6160 = 2.5675

logY = Anti log 2.5675 = 369.4

Hence the estimated sale for the year 1972 is 385.9 thousand rupees

Problem 4: Find the coefficient of correlation between X and Y

X 1 2 3 4 5 6 7 8 9Y 12 11 13 15 14 17 16 19 18

Solution Observations TOTALx 1 2 3 4 5 6 7 8 9 45y 12 11 13 15 14 17 16 19 18 135x2 1 4 9 16 25 36 49 64 81 285y2 144 121 169 225 196 289 256 361 324 2085xy 12 22 39 60 70 102 112 152 162 731

Correlation Coefficient =

R= 504/540 = .933 strong relation.

R= n (∑ X Y) - ( ∑ X ) ( ∑ Y )

[ n ( ∑ X2) - ( ∑ X )2 ] [ n ( ∑ Y2 ) - ( ∑Y )2 ]

R = 9(731)-(45)(135)

(9(285)-(45)2)(9(2085)-(135)2)

Problem 5: The following are the index of annual production of a certain commodity, assume 5 yearly cycles, and find out the trend values.

Year 1941 1942 1943 1944 1945 1946 1947 1948 1949

Index 225 210 201 215 223 245 235 225 233

Year 1950 1951

Index 249 265

Solution

Year X Index 5 Years Moving total 5 Years moving average as trend values

1941 1 225 1942 2 210 1943 3 201 1074 214.81944 4 215 1094 218.81945 5 223 1119 223.81946 6 245 1143 228.61947 7 235 1161 232.21948 8 225 1187 237.41949 9 233 1207 241.41950 10 249 1951 11 265

Assignments - B

Q 1: A die is tossed 120 times with the following results:

No. turned up

1 2 3 4 5 6 Total

Frequency 30 25 18 10 22 15 120

Test the hypothesis that the die is unbiased.

Solutions:

Number of turn

Frequency ProbabilityExp

frequencyChi Square

1 30 0.166 19.92 5.10072289

2 25 0.166 19.92 1.29550201

3 18 0.166 19.92 0.18506024

4 10 0.166 19.92 4.94008032

5 22 0.166 19.92 0.21718876

6 15 0.166 19.92 1.21518072

Total 120 1 119.52 12.9537349

Calculated value of chi square 12.95 is greater than tabulated value which is 5.226, so the die is not fair.

Q 2: Ballast must weigh 150 kg. It can be made from two raw materials, A (with a cost of Rs. 20 per unit) and B (with a cost of Rs. 80 per unit). At least 14 units of B and no more than 20 units of A must be used. Each unit of A weighs 5 kg and each unit of B weighs 10 kg. How many units of each type of raw material must be used for a product to minimize cost?

Solutions:

Using linear programming, 14 units of B and 2 unit of A should be used to minimize cost.Interpret the problem: B >= 14 A <= 20 5A + 10B = 150 Cost = 80B + 20A

Since we at least have to have 14 units of B, which will only leave 10 kg remaining. Since it is cheaper to have 2 As than 1B, it should be 14 Bs and 2 As

Q3: A company is trying to decide whether to bid for a certain contract or not. They estimate that merely preparing the bid will cost Rs. 10,000. If their company bid then they estimate that there is a 50% chance that their bid will be put on the "short-list", otherwise their bid will be rejected. Once "short-listed" the company will have to supply further detailed information (entailing costs estimated at Rs.5,000). After this stage their bid will either be accepted or rejected. The company estimates that the labor and material costs associated with the contract are Rs. 127,000. They are considering three possible bid prices, namely £155,000, £170,000 and £190,000. They estimate that the probability of these bids being accepted (once they have been short-listed) is 0.90, 0.75 and 0.35 respectively. What should the company do and what is the expected monetary value of your suggested course of action?

Solutions:

1 2 3TOTAL COST 142,000 142,000 142,000BID PRICES 155000 170000 190000PROFIT 13,000 28,000 48,000PROBABLITY OF PROFIT 0.9 0.75 0.35ESTIMATED PROFIT 11700 21000 1680050%CHANCE INTIAL COST 5000 5000 5000 6700 16000 11800

The company should go for bidding with the price of £170,000 keeping in view the profitability of £16,000.

Case Study

The Department of Environment has theorized that pollution levels are higher in winter (I & IV Quarter) than summer (II & III Quarter) and that they are increasing over the years. The following data was collected:Quarter I II III IV 1996 293 246 231 282 1997 301 252 227 291 1998 304 259 239 296 1999 306 265 240 300Problem:a. Determine the seasonal indices and deseasonalize the data. b. Calculate the regression line that is described by this data. c. Are both the assumptions of the department of Environment correct? You may test to a significance level of 0.05.

FOUR MONTH MA CMA

RATIO TO MA

DESEASONALIZED DATA USING 

SEASONAL INDEX1995 1 293 262

2 246 263 2593 231 265 264 0.88 2684 282 267 266 1.06 263

1996 1 301 266 266 1.13 2692 252 268 267 0.95 2663 227 269 268 0.85 2634 291 270 269 1.08 272

1997 1 304 273 272 1.12 2722 259 275 274 0.95 2733 239 275 275 0.87 2774 296 277 276 1.07 276

1998 1 306 277 277 1.11 2742 265 278 277 0.96 2793 240 2784 300 280

MEAN TO MA SEASONAL INDEX1 1.12 1.122 0.95 0.953 0.86 0.864 1.07 1.07

SUM 4.0032

NORMALIZATION RATIO 0.999212331

Y X XY X2 TREND LINE293 1 293 1 264246 2 492 4 265231 3 693 9 266282 4 1128 16 267301 5 1505 25 268252 6 1512 36 269227 7 1589 49 269291 8 2328 64 270304 9 2736 81 271259 10 2590 100 272239 11 2629 121 273296 12 3552 144 274306 13 3978 169 275265 14 3710 196 276240 15 3600 225 277300 16 4800 256 2784332 136 37135 1496

SSX 340SSXY 313Bi 0.92Bo 263YMEAN 270.75XMEAN 8.5 Y=263+.92X

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig.

95.0% Confidence Interval for B

BStd. Error Beta

Lower Bound

Upper Bound

1 (Constant) 262.925 15.406 17.067

.000 229.883 295.967

QUARTER

.921 1.593 .153 .578 .573 -2.497 4.338

a. Dependent Variable: POL.LEVEL

Using the significance level test, the result showed that the null hypothesis is not rejected

and both the assumptions are correct.

Assignment -C

1. If A and B are independent events with P (A) = 0.25, P (B) =0.4 and P (A UB) = 0.5,

then, P (A/B) & P (B/A) are

a. 0.25 & 0.4

b. 0.600 & 0.275

c. 0.725 & 0.275

d. 0.650 & 0.650

e. 0.542 & 0.335

2. If you want to test the whether the change is significant on the mean body weight on

group of randomly chosen people after a particular diet is administered, you should

employ

a. Paired-t test

b. A simple t test

c. An independent single sample t test

d. An independent two sample t test

e. Variance test

3. Cluster sampling is

a. a non-probability sampling method

b. the same as convenience sampling

c. a probability sampling method

d. Judgement sampling

e. None of these alternatives is correct.

4. A LP problem has 3 decision variables and 5 constraints. How many non basic

variables are there?

a. 3

b. 5

c. 8

d. 7

e. 2

5. If a random variable X is distributed normally with mean 30 and variance 25, find oi

P(X>40)

a. 0.2220

b. 0.0228

c. 0.0954

d. 0.0233

e. 0.0919

6. A sampling method in which the population is divided into groups such that each

group has a small variation with in itself and a wide variation between themselves and

samples are drawn from each group is known as

a. Random sampling

b. Stratified sampling

c. Cluster sampling

d. Systematic sampling

e. Judgmental sampling

7. The following linear trend expression was estimated using a time series with 17 time

periods.

Tt= 129.2 + 3.8t

The trend projection for time period 18 is

a. 68.4

b. 193.8

c. 197.6

d. 6.84

e.19.38

8. If the sampling fraction n/N is less than 0.05, the standard error of the sample mean is

given by

a. / n

b. / n x n 1

c. / n x n

d. / n x n

e.

9. The sample mean is the point estimator of : Ans (Population mean µ)

a. µ

b. σ

c. x

d. p

e. S

10. A regression analysis between sales (Y in $1000) and advertising (X in dollars)

resulted in the following equation

Y$ = 30,000 + 4 X

The above equation implies that an

a. Increase of $4 in advertising is associated with an increase of $4,000 in sales

b. Increase of $1 in advertising is associated with an increase of $4 in sales

c. Increase of $1 in advertising is associated with an increase of $34,000 in sales

d. Increase of $1 in advertising is associated with an increase of $4,000 in sales

e. Increase of $4 in advertising is associated with an increase of $30,000 in sales

11. A random Variable has the following probability distribution:

X P(X)

0 0.05

1 0.1

2 0.15

3 0.20

4 0.25

5 0.10

6 0.15

What is the value of P(l<= X<=5)?

a. 0.80

b. 0.25

c. 0.15

d. 0.10

e. 0.30

12. Two cards are drawn without replacement from a deck of 52 cards. What is the

probability of drawing two queens?

a. 1/221

b. 1/121

c. 1/321

d. 1/421

e. 1/111

13. Assume a binomial probability distribution with n = 40 and p = .55. Compute the

mean and standard deviation of the random variable.

a. Mean = 22 and SD = 3.146

b. Mean = 20 and SD = 3.146

c. Mean = 24 and SD = 3.146

d. Mean = 26 and SD = 3.146

e. Mean= 18 and SD = 3.146

14. From a calendar for 2005 we sample every 11th day starting from January 7th;

what type of sampling is this?

a. Judgemental sampling

b. Simple random sampling without replacement

c. Systematic sampling

d. Cluster sampling

e. Simple random sampling with replacement

15. In a goodness-of-fit test where the sample size is 200, there are 5 categories, and

the significance level is .05. The critical value of %2 is

a. 9.488

b. 11.070

c. 43.773

d. 45.887

e. 25.669

16. To conduct the sign test, we assume

a. The population is normally distributed

b. The scale of measurement is interval

c. The samples are dependent

d. There are at least 20 observations in the sample

e. There are minimum 25 observations in the sample

17. A time series component which cannot be analysed by a mathematical model is:

a. Trend

b. Seasonal

c. Cyclical

d. Random

e. Cyclical and random

18. Which of the following cannot be inferred from a scatter diagram?

a. Cause effect relationships

b. Presence or absence of relationships

c. Linear or curvilinear relationship

d. Direct or inverse relationship

e. All can be studied

19. Which of the following is true of the coefficient of determination?

a. It is the square of the correlation coefficient

b. It conveys the extent to which the variations are explained by the regression

equation

c. It conveys the extent to which the variations are unexplained by the regression

equation

d. Both (a) and (b) above

e. Both (a) and (c) above

20. When formulating Transportation LP problems, constraints usually deal with:

a. The number of items to be transported

b. The shipping costs associated with transporting goods

c. The distance goods are to be transported

d. The number of origins and destinations

e. The capacities of origins and requirements of destinations

21. If the coefficient of correlation between two variables X and Y is equal to one,

then there is

a. No relationship between variables X and Y

b. A perfect positive linear relationship between variables X and Y

c. A perfect negative linear relationship between variables X and Y

d. A cause and affect relation exists between X and Y

e. A weak association between variables X and Y

22. An inventor claims that her new petrol additive will drastically enhance the

mileage of the petrol powered cars. Currently, the vehicle runs as average mileage

15 km for one litre of petrol. The appropriate null and alternative hypotheses in

evaluating her claim will be (in the order of HO and Ha)

a. X=15, X> 15

b. X=15,X<15,

c. X>15,X=15

d. X=15,X=15,

e. X= 15, X = < 15

23. After deseasonalisation, a time series can be represented as

a. Y = S x C x I

b. Y = TxSxCxI

c. Y = TxCxI

d. Y = TxSxI

e. Y = TXSXC

24. If one regression coefficient is greater than unity then the other must be:

a. Greater than the first one

b. Equal to unity

c. Less than unity

d. Equal to zero

e. Less than the first one

25. Which of the following statements is false?

a. In a proper random sampling, every element of the population has a known (and

often equal) chance of being selected

b. The precision of a sample mean or sample proportion depends only upon the

sample size (and not the population size) in a proper random sample

c. Convenience sampling often leads to biases in estimates since the sample is often

not representative of the population

d. If a sample of 1000000 families is randomly selected from all of Kota (with about

8000000 families) and the average family income is computed, then the true value

of the family income for all families in Kota is known

e. None of the above

26. For two variables x and y to be independent of each other which of the following

must be true

a. x y

b. x

y

c. Cov (x, y) = 0

d. =

e. E(x) = E(y)

27. Which of the following is a true measure of regret?

a. Maximum possible profits - realized profits

b. Maximum of minimum profits - minimum of minimum profits

c. Maximum possible profits - foregone profits (probably)

d. Maximum of maximum profits - maximum of minimum profits

e. Maximum possible profits - minimum of maximum profits.

28. A sample of 15 is drawn from a population size of 100. The finite population

correction factor is

a. 0.150

b. 0.184

c. 0.523

d. 0.834 (I think it should be 0.86)

e. 0.9266

29. Which of the following represents repetitive and predictable movements around

the trend line within a time period of one year or less?

a. Secular trend

b. Cyclical fluctuation

c. Seasonal variation

d. Irregul ar vari ati on

e. Temporary variation.

30. Which of the following is true with respect to the method of least squares?

a. Sum of the squared values of the horizontal distances from the regression line to

the y-axis and the corresponding points of the dependent variable is minimized

b. Sum of the squared values of the vertical distances from the regression line to

the x-axis and the corresponding points of the independent variable is

minimized

c. Sum of the squared values of the horizontal distance from each plotted point

based on the observations to the regression line is minimized

d. Sum of the squared values of the vertical distance from each plotted point to

the regression line is minimized

e. None of the above.

31. The probability that an observation, following a normal distribution, will lie within [i

± 1.3a is

a. 9.5 %

b. 19.0%

c. 40.3%

d. 50.0%

e. 80.6%

32. Arrivals of customers at an ATMs follow the Poisson distribution. The average

arrivals per hour is 6. The probability of exact 6 arrivals in an hour is

a. 1.00

b. 0.50

c. 0.25

d. 0.16

e. 0.10

33. If a random sample of size 15 is selected from a symmetrical population with a

unique mode, the degrees of freedom of the observation is

a. 14

b. 15

c. 16

d. 17

e. 18

34. In regression analysis, represents how much each unit change of the independent

variable changes the dependent variable.

a. Slope

b. Y - intercept

c. Standard error of estimate

d. Dependent variable

e. Coefficient of correlation

35. If two variables X and Y are perfectly positively correlated and their standard

deviations are 5 and 10 respectively, then the covariance is

a. 0.40

b. 0.50

c. 2.00

d. 4.00

e. 50.00

36. The sample proportion of ripe mangoes in a large consignment is 0.7. If the upper

limit of a confidence interval for the proportion of ripe mangoes in the lot is 0.86, the

lower limit is:

a. 0.64

b. 0.54

c. Depends on the confidence level

d. Depends on the sample size

e. Both (c) and (d) above

37. A contingency table for two attributes consists of 24 cells. The number of degrees of

freedom for the chi square test statistic is:

a. Depends on the number of rows and columns

b. 24

c. 23

d. 14

e. 15

38. Which of the following statements are true? (I am not sure)

a. When the percent of trend is below 100, the relative cyclical trend is negative and

conversely

b. When the percent of trend is below 100, the relative cyclical trend is positive

and conversely

c. When the percent of trend is below 100, the relative cyclical trend is negative but

not conversely

d. When the percent of trend is below 100, the relative cyclical trend is positive but

not conversely

e. The two measures have to be considered independently

39. Which of the following is not true of random variations?

a. They can be identified

b. It cannot be explained mathematically

c. They occur in a random manner

d. They cannot be easily predicted

e. All are true

40. The loss from stocking a unit of a product not sold is Rs.30 while the profit from

selling a unit of that product is Rs.50. The minimum probability of selling an extra unit

that will justify stocking it is:

a. 3/5

b. 2/5

c. 3/8

d. 2/8

e. 3/4