F-2,Block, Amity CampusSec-125, Nodia (UP)

India 201303

ASSIGNMENTSPROGRAM:SEMESTER-ISubject Name : Quantitative Applications in Management and Research

Study COUNTRY : SudanPermanent Enrollment Number (PEN) :Roll Number : IB01652010-2012045Student Name : SOMAIA TAMBAL ELMALIK

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

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

b) Total weightage given to these assignments is 30%. OR 30 Marksc) 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 attached a scan signature in the form.

Signature :Date : _____15.AUG.2011____________________________

( √ ) Tick mark in front of the assignments submitted

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

Quantitative Applications in Management and Research

Assignment –A

Ques.1 Comment on “Quantitative Techniques is a scientific and for enhancing creative and judicious capabilities of a decision maker”, also state the different elements of Decision.

Yes you can that because Managerial decision-making is a process by which management, when faced with a problem,chooses a specific course of action from a set of possible options. In making a decision, a business manager attempts to choose that course of action which is most effective in the given circumstances in attaining the goals of the organization. The various types of decision-making situations that a manager might encounter can be listed as follows.1. Decisions under certainty where all facts are known fully and for sure or uncertainly where the event that would actually occur is not known but probabilities can be assigned to various possible occurrences.2. Decisions for one time-period only called static decisions, or a sequence of interrelated decisions made either simultaneously or over several time periods called dynamic decisions.3. Decisions where the opponent is nature (digging an oil well, for example) or a national opponent (for instances, setting the advertising strategy when the actions of competitors have to be considered)These classes of decisions-making situations are not mutually exclusive and a given situation would exhibit characteristics from each class. Stocking of an item for sale in a certain trade fair, for instance, illustrates a static decision making situation where uncertainly exists and nature is the opponent.

Ques. 2 The raw data displayed here are the scores (out of 100 marks) of a market survey regarding the acceptability of a new product launch by a company for a random sample of 50 respondents

40 45 41 45 45 30 39 8 4825 26 9 23 24 26 29 8 4041 42 39 35 18 25 35 40 4243 44 36 27 32 28 27 25 2638 37 36 35 32 38 40 41 4344 45 40 39 41

a. Form a frequency distribution having 9 class intervals

No. Classes frequency1. 5 – 10 32. 10 - 15 03. 15 – 20 1 4. 20 – 25 25. 25 – 30 106. 30 – 35 27. 35 – 40 128. 40 – 45 159. 45 – 50 5

b. Form a percentage distribution from the frequency distribution (from part a)No. Classes frequency Percentage distribution1. 5 – 10 3 62. 10 - 15 0 03. 15 – 20 1 24. 20 – 25 2 45. 25 – 30 10 206. 30 – 35 2 47. 35 – 40 12 248. 40 – 45 15 309. 45 – 50 5 10

c. Form a histogram, frequency polygon and frequency curve of the frequency distribution (from part a)

Histogram figure as follow :

frequency curve :

Ques.3 Compute the mean, standard deviation and Coefficient of variation of the following data and comment on the result

Size Frequency12.513.013.514.014.515.015.516.0

41930636629181

Mean = Σ f*x / N = 87.16

Standard deviation = σ = √[(Σfx2/Σf) – (Σfx/ Σf)2] = √[(46633.5/230) – (20047/ 230)2] =√[( 202.75) – ( 87.16)2] = 10.75 Coefficient of variation ( CV ) = S . 100/ Xmean=1.2

Ques.4 Following figures give the rainfall in inches for the year and the production in 00’ of Kgs. For the Rabi crop and Kharif crop. Calculate the Karl Pearson’s coefficient of correlation, between rainfall and total production and comment on the result.

Rainfall Rabi Production Kharif Production20 15 1522 18 1724 20 2026 32 1828 40 2030 39 2132 40 15

The correlation between rainfall and rabi production is :No. X

(Rainfall) Y ( Rabi production)

( x-26) ( y-29.1)

( x-26) ( y- 29.1)

1. 20 15 -6 - 14.1 84.62. 22 18 -4 -11.1 44.43. 24 20 -2 -9.1 19.84. 26 32 0 2.9 05. 28 40 2 10.9 21.86. 30 39 4 9.9 39.67. 32 40 6 10.9 65.4Total 257.6

The mean of x = 26The mean of y = 29.1Cov ( x, y)= 257.6 / 7= 36.8N= 7 Sx = 4.32 Sy = 11.17R = 36.8 / (4.32 * 11.17) = 36.8 / 48.25 = 0.76 The relation between rainfall and rabi production is perfect and positiveThe correlation between rainfall and kharif production is :No. X

(Rainfall) Y ( kharif production)

( x- 26)

( y- 18) ( x-26) ( y- 18)

1. 20 15 -6 -3 182. 22 17 -4 -1 43. 24 20 -2 2 44. 26 18 0 0 05. 28 20 2 2 46. 30 21 4 3 127. 32 15 6 -3 -18Total 24

The mean of x = 26The mean of y = 18Cov ( x,y) = 24 / 7= 3.43Sx = 4.32 Sy = 2.45 R = 3.43 / (4.32 * 2.45) = 3.43 / 10.584 = 0.324

Ques.5 The marks obtained by Nine students in Physics and Mathematics are given below:

Marks in Physics: 35 23 47 17 10 43 9 6 28Marks in Mathematics:30 33 45 23 8 49 12 4 31Compute their ranks in the two subjects and coefficient of correlation of ranks.By using Spearman‘s Rank-correlation coefficient :

No. Physics

Ranks(d.1)

Mathematics

Ranks(d.2)

d1 =( r1 – r2)

d2

1. 35 3 30 5 -2 42. 23 5 33 3 2 43. 47 1 45 2 -1 14. 17 6 23 6 0 05. 10 7 8 8 -1 16. 43 2 49 1 1 17. 9 8 12 7 1 18. 6 9 4 9 0 09. 28 4 31 4 0 0Total

12

R= =0.9N=9

Assignment –B

Ques.1 i. Define Binomial, Poisson and Normal distribution.Poisson DistributionThe Poisson distribution is generally used when measuring the number of occurrences of something (# of successes) over an interval or time period.The assumptions of a Poisson probability distribution are: The probability of the occurrence of an event is constant for all subintervals.There can be no more than one occurrence in each subinterval. Occurrences are independent; that is, the number of occurrences in any non-overlapping intervals is independent of one another.Normal Distribution or Normal Curve: Normal distribution is probably one of the most important and widely used continuous distribution. It is known as a normal random variable, and its probability distribution is called a normal distribution.

ii. Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting

a. all the four cards of the same suitAnswer: P = p1.p2.p3.p4= 1/4 X 1/4 X 1/4 X 1/4 = 0.0039

b. all the four cards of the same numberAnswer: P= 4/52 X 3/51 X 2/50 X 1/49 =

= 0.0769 X 0.0588 X 0.04 X 0.0204 = 0.00000369

c. one card from each suitAnswer: p = 4/52 (1/4 X 1/4 X 1/4 X 1/4) = 0.0003

d. two red cards and two black cardsAnswer: p = 2/52 X 2/50 = 0.038 X 0.04 = 0.00152

e. all cards of the same colourAnswer: p 4/52 X 1/13 = 0.077 X 0.077= 0.005989

f. all face cardsAnswer: p = 4/52 X 1/12 = 0.077 X 0.083 = 0.0064

Ques.2 The following table gives the aptitude test scores and productivity indices of 10 workers selected at random:

Aptitude scores(X) 60 62 65 70 72 48 53 73 65 82Productivity index(Y) 68 60 62 80 85 40 52 62 60 81

Calculate the two regression equations and estimatea. The productivity index of a worker whose test score is 92b. The test score of a worker whose productivity index is 75

No. Aptitude scores(X)

Productivity index(Y)

x*y X2

1. 60 68 4080 36002. 62 60 3720 38443. 65 62 4030 42254. 70 80 5600 49005. 72 85 6120 51846. 48 40 1920 20347. 53 52 2756 28098. 73 62 4526 53299. 65 60 3900 422510. 82 81 6642 6724Total 650 650 43294 36150

Y = a + bX =ΣX = 650 Σ Y = 650 Σ XY = 43294 Σ X2 = 36150 Σ XY = a Σ X + Σ X2

43294 = a * 650 + 36150 43294 - 36150= a650 = a= 7144/650= 10.99

Answer,B :ΣY = na +b Σ X 650 = 10 *10.99 + b * 650 650 – 109.9 = b650= 0.83

The equation :Y = 10.99 + 0.83X

A: The productivity index of a worker whose test score is 92 :While x = 92 y is :Y = 10.99 + 92 * 0.83 = 87.4

The test score of a worker whose productivity index is 75: Y = 75 X 75 = 10.99 + 0.83 X X = 77.12

Ques.3 Discuss the different components of a time series and fit a trend line with the help of following data by using Free hand curve method and Semi-averages method:

Year 1993 94 95 96 97 98 99 2000 01 02 03 04Profit 10 12 16 8 6 14 15 10 14 20 13 18(Rs. in lakhs).

Freehand method:

Freehand method Advantages 1. The Freehand method is a very simple method of estimating trend. 2. There is flexibility in this method as it can be used regardless whether the trend is a straight line or non-linear. 3. If the statistician is well-conversant with the movement of the particular variable involved in the time series, the use of this method may even give a better expression to the long-term movement than the trend fitted by a rigid mathematical formula. Limitations 1.This is a highly subjective method as the trend line fitted to the same set of data by this method will vary from one person to another. 2. In view of the trend line being highly subjective, it is not an appropriate method for making predictions. 3. It means very long experience on the part of the statistician to use this method, otherwise, the trend fitted would not be of much use.

The method of semi-averages :When the method of semi-averages is used, the given time series is divided into two parts preferably with the same number of years. The average of each part is calculated and then a trend line through these averages is fitted. This is illustrated with the data given in Table:

Year X Y Average1993 0 101994 1 121995 2 16 1996 3 81997 4 61998 5 14 66/6=111999 6 152000 7 102001 8 142002 9 202003 10 132004 11 18 90/6=15

1) The average of first part of the data is 11 and that of the second part is I5. Since 11 is the average of1993, 1994, 1995, 1996 , 1997and1998 11 is plotted in between 1997 and 1998, which is the middle of the 6-year period. Likewise, 15 is plotted in between

2) 2003 and 2004. Then these points are joined by a straight line, which is a semi-average trend line. Advantages 1. The method of semi-averages is simple to use as anyone can use it conveniently. 2. This is an objective method as anyone applying it to the given set of data would get the same trend line. Limitations 1. This method will always give a straight line trend regardless of the nature of the given set of data. Thus, it assumes a straight line relationship, which may not be true. 2. This method may give wrong trend-line on account of the limitations of arithmetic average. In case there is an extreme value in either half or both halves of the time series, then the trend line will not give a realistic growth of the phenomenon being measured. In order to overcome this problem, it is necessary to ensure that the data do not have extreme values.

A time series: Is a chronological sequence of observations on a particular variable. Usually the observations are taken at regular intervals (days, months, years), but the sampling could be irregular. A time series analysis consists of two steps:

(1) building a model that represents a time series. (2) using the model to predict (forecast) future values. The time-series can be represented as a curve that evolves over time. Forecasting the time-series mean that we extend the historical values into the future where the measurements are not available yet. There are some subtleties in the definition a time-series forecast. For example, the historical data might be daily sales and but you need monthly forecasts. Grouping the values according to a certain period (ex: month) is called time-series. The following are few examples of time series data: 1. Profits earned by a company for each of the past five years. 2. Workers employed by a company for each of the past 15 years. 3. Number of students registered for the MBA programme of an institute for each of the past five years. 4. The weekly wholesale price index for each of the past 30 weeks. 5. Number of fatal road accidents in Delhi for each day for the past two months.Role of time Series 1. A time series analysis enables one to study such movements as cycles that fluctuate around the trend. Knowledge of cyclical pattern in certain series of data will be helpful in making generalizations in the concerned business or industry. 2. The analysis of a time series enables us to understand the past behavior or performance. We can know how the data have changed over time and find out the probable reasons responsible for such changes. If the past performance, say, of a company, has been poor, it can take corrective measures to arrest the poor performance.

3. A time series analysis helps directly in business planning. A firm can know the long-term trend in the sale of its products. It can find out at what rate sales have been increasing over the years. This may help it in making projections of its sales for the next few years and plan the procurement of raw material, equipment and manpower accordingly.

4. A time series analysis enables one to make meaningful comparisons in two or more series regarding the rate or type of growth. For example, growth in consumption at the national level can be compared with that in the national income over specified period. Such comparisons are of considerable importance to business and industry. 5. A time series analysis helps in evaluating current accomplishments. The actual performance can be compared with the expected performance and the cause of variation analyzed e.g. if we know how much is the effect of seasonality on business we may device ways and means of ironing out the seasonal influence or decreasing it by producing commodities with complementary seasons.Components of a time series

1 Secular Trend - the smooth long term direction of a time series

2 Seasonal Variation - Patterns of change in a time series within a year which tends to repeat each year

3 Cyclical Variation - the rise and fall of a time series over periods longer than one year

4 Irregular Variation - classified into:

Episodic - unpredictable but identifiable Residual - also called chance fluctuation and unidentifiable

Case Study

The marks obtained by seven students in Statistics and Accountancy are as follows:

Age(X) 56 42 36 47 49 42 60 72 63 55

Blood 147 125 118 128 145 140 155 160 149 150Pressure(Y)

SOLUTION:i.Given the form of the scattered diagram, does it appear that a straight line provides an accurate model for the data?

ii.Find the correlation coefficient between Age(X) and Blood Pressure(Y) and discuss its nature.

No. X Y

(X - X Mean) *(Y -Y Mean)

X * Y

1. 56 147

20.14 8232

2. 42 125

170.34 5250

3. 36 118

383.94 4248

4. 47 128

71.24 6016

5. 49 145

10.56 7105

6. 42 140

17.34 5880

7. 60 155

103.74 9300

8. 72 160

362.34 11520

9. 63 149

78.84 9387

10. 55 150

23.24 8250

Total 1241.72 75188

Answer: ii.X Mean = 52.2Y Mean = 141.7 Cov = Σ (X - X Mean) *(Y -Y Mean)/ n = 1241.72/ 10 = 124.172Sx = 11.05Sy = 13.76

R= 124.172 /11.05 * 13.76 = 124.127/152.048 = 0.82The relation between age (x) and blood pressure is positive and strong .

iii. Find the two lines of regression.Answer: iii. The equation for a straight line is:Y =a + bXΣXY = a ΣX + ΣX2 :. A= ΣXY- ΣX2 / ΣX ΣX= 522 ΣX2= 28,348 ΣXy= 75188A= 28348-75188 /522 = 89.7 B: ΣY = na +b Σ X ΣY= 1417 n= 10 a= 89.7 Σx = 522

1417= 10*89.7 + b* 522 = 1417-897 = b* 522 B= 0.996So the equation is : Y= 89.7 + 0.996 x

iv. Estimate the blood pressure of a woman whose age is 45

The blood pressure of a woman whose age is 45 is :x= 45 y = 89.7 + 0.996 * 45 = 134.52 The blood pressure of a woman whose age is 45 is 134.52

Assignment –C

Ques.1 a sequence of interrelated decisions made either simultaneously or over several time periods called dynamic decisions.

a. dynamic decisions(√) b. static decisionsc. Both d. None

Ques.2 Stocking of an item for sale in a certain trade fair, illustrates a

a. Static decision b. Where uncertainly exists c. Nature is opponent.

d. All of above(√)

Ques.3 Quantitative analysis is also called

a. Operations researchb. Management science

c. Quantitative techniques

d. All the above(√)

Ques.4 Quantitative research provides the fundamental connection between

a. empirical observation and mathematical expression(√)b. empirical observation and qualitative expressionc. empirical observation and social expressiond. empirical observation and all expression

Ques.5 Most of the business decisions can be made on the basic of

a. Rule of thumbb. Commonsense c. Snap judgment.

d. Quantitative Techniques(√)

Ques.6 Statistics is a branch of

a. applied physics

b. applied mathematics(√)c. applied commerced. Dramatics

Ques.7 The mean of 7, 12, 24, 20, 19 is

a. 14b. 16c. 15.4

d. 16.4(√)

Ques.8 ∑ (X/c) =

a. ∑ ( X)/n cb. ∑ ( X)/∑ c

c. ∑ ( X)/c(√)d. X/c.

Ques.9 Midterm exam scores for a small advanced neuroanatomy class are provided below. Scores represent percent of items marked correct on the exam. 87,99,75,87,94,75,35,88,87,93The mode of the distribution

a. 75

b. 87(√)c. 88d. 94

Ques.10 Which measure of Central tendency is most efficient

a. Mean(√)b. Medianc. Moded. All are equale.

Ques.11 Mean Deviation can be calculated from

a. Mean(√)b. Medianc. Mode.

d. All the three

Ques.12 Qualitative data are

a. Non-numeric(√)b. Numericc. Can be both d. None

Ques.13 The numeric data that have a finite number of possible values is calleda. Continuous data

b. Discrete data(√)c. Datumd. None

Ques.14 The Coefficient of Variance is expressed as

a. CV = .S . X 100(√) Xmean

b. CV = .S . Xmean

c. CV = . Xmean . X 100 S

d. CV = (X - Xmean )

Ques.15 Which one is unaffected by extreme scores

a. Mean

b. Median(√)c. Moded. Range

Ques.16 A storeowner kept a tally of the sizes of suits purchased in her store. Which measure of central tendency should the storeowner use to describe the average suit sold?

a. Mean(√)b. Medianc. Moded. None

Ques.17 The correlation coefficient, r = -1, implies

a. Perfect negative(√)b. Perfect positivec. No correlationd. Limited correlation

Ques.18 If two variables changes in the opposite direction and in the same proportion, the correlation between the two is

a. Perfect positiveb. Limited positivec. Limited Negative

d. Perfect negative(√)

Ques.19 The value of ‘r’ gives the magnitude of correlation and its sign denotes its

a. Value

b. Direction(√) c. Bothd. None

Ques.20 By the Rank method the value of R is -0.73 it suggests a

a. fairly strong negative relationship(√)b. fairly strong positive relationshipc. Perfect negatived. Perfect positive

Ques.21 The range of the correlation coefficient is?

a. -1 to 0. b. 0 to 1.

c. -1 to 1.(√) d. None of the above.

Ques.22 When looking at a sequence of monthly postal revenue data, we note that the revenue is consistently highest in December. The high December revenue is an illustration of:

a. trend

b. seasonal variation(√)c. irregular fluctuationsd. a cycle

Ques.23 Which of the following is NOT an assumption of the Binomial distribution?

a. All trials must be identical.(√)b. All trials must be independent.c. Each trial must be classified as a success or a failure.d. The probability of success is equal to .5 in all trials.

Ques.24.In Regression Analysis the independent variable is also known as

a. Regressed variable(√)b. Regressor variablec. Random variabled. All of the above

Ques.25.Given that we have collected pairs of observations on two variables X and Y , we would consider fitting a straight line with X as an explanatory variable if:

a. the change in Y is an additive constant.

b. the change in Y is a constant for each unit change in X(√)c. the change in Y is a fixed percent of Yd. the change in Y is exponential

Ques.26 In Regression Analysis, a single regression line is obtained in case if

a. r = +1b. r = -1

c.r = +1(√)c. r = 0

Ques.27 The regression Analysis Studies

a. one-way causal effectb. two-way causal effectc. interdependence of the variables

d. dependence of the variables(√)

Ques.28 Correlation Coefficient is the ---------------between the regression coefficients

a. arithmetic mean

b. geometric mean(√)c. harmonic meand. median

Ques.29 Gradual shifting of a time series over a long period of time is called

a. periodicity. b. cycle. c. regression.

d. trend.(√)

Ques.30 The trend component is easy to identify by using

a. moving averages(√) b. exponential smoothing c. regression analysis d. the Delphi approach

Ques.31 Seasonal components

a. cannot be predicted.

b. are regular repeated patterns.(√) c. are long runs of observations above or below the trend line. d. reflect a shift in the series over time.

1. Ques.32 What probability is shown on the Venn diagram by the shaded region below t probability is shown on the Venn diagram below

a. a. p(A)b. b. p(B)

c. p(A and B)

d. p(not B)(√)

Ques.33 At Sanjay Middle School, 3 out of 5 students make honor roll. What is the probability that a student does not make honor roll?

a. 65%

b. 40%(√)c. 60%d. None of the above

Ques.34 In a class of 30 students, there are 17 girls and 13 boys. Five are A students, and three of these students are girls. If a student is chosen at random, what is the probability of choosing a girl or an A student?

a. 19/30

b. 11/50(√)c. 12/30d. 15/40

Ques.35   In a shipment of 100 televisions, 6 are defective. If a person buys two televisions from that shipment, what is the probability that both are defective?

a. 3/100(√)b. 1/330c. 9/2500d. 6/100

Ques.36 Find the correlation coefficient r(X, Y) between X and Y,whenCov(X,Y) = -2.45, Var (X) = 8.25 and Var (Y) = 21.49

a. 0.18

b. – 0.18(√)c. 0.36d. – 0.36

Ques.37 A coin is tossed 5 times. What is the probability of getting atleast 3 heads?

a. 1/2b. 1/3c. 1/4

d. 1/5(√)

Ques.38 Normal Distribution is symmetrical about its

a. Harmonic mean

b. Mean(√)c. Ranged. Standard deviation

Ques.39 In Normal Distribution 95% of the observations fall within 2 standard deviations of the mean, that is, between

a. µ - σ and µ +σ

b. µ - 2σ and µ +2σ(√)c. µ - 3σ and µ +3σd. Not defined

Ques.40 Condition for the Applicability of Binomial Distribution:

a. There should be a finite number of trials.b. The trials do not depend on each other.c. Each trial should have only two possible outcomes, either a success or a failure.

d. All of the above(√)