F-2,Block, Amity Campus

Sec-125, Nodia (UP)

India 201303

ASSIGNMENTS PROGRAM:

SEMESTER-I Subject Name : Quantitative Applications in Management and Research

Study COUNTRY : BOTSWANA

Permanent Enrollment Number (PEN) : A400020141038

Roll Number : IB01112014-20160144

Student Name : GASEFELE L ORAPELENG

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 10

Assignment 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 attached a scan signature in the form.

Signature : _ ________________________________

Date : ____16/01/2015_____________________________

( √ ) 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. In making a decision, a decision maker uses a scientific approach/methodologies to make suitable decisions. The decision maker chooses that courses of action which is most effective in the given circumstance. Quantitative Technique is there a science as the decision maker might encounter the following types of decision making situations:

A decision under certainty where all facts are fully known and for sure uncertainly where the events that would actually occur is not known but probability can be assigned to various possible occurrences.

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.

ELEMENT OF A DECISION: - A decisions maker who could be an individual, group, organization or society - A set of possible actions that may be taken to solve the decision problem - A set of possible states that might occur - A set of consequences associated with various combinations of courses of action and the states that may

occur - The relationship between the pay offs and the values of the decision maker

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 48 25 26 9 23 24 26 29 8 40 41 42 39 35 18 25 35 40 42 43 44 36 27 32 28 27 25 26 38 37 36 35 32 38 40 41 43 44 45 40 39 41

a. Form a frequency distribution having 9 class intervals FREQUENCY DISTRIBUTIONS

RANGE FREQUENCY

0-10 3

10-20 1

20-30 13

30-40 18

40-50 15

b. Form a percentage distribution from the frequency distribution (from part a)

PERCENTAGE DISTRIBUTION

RANGE FREQUENCY PERCENTAGE

0-10 3 6%

10-20 1 2%

20-30 13 26%

30-40 18 36%

40-50 15 30%

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

ii.

iii.

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

Size Frequency

12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0

4 19 30 63 66 29 18 1

COMPUTING THE MEAN, STANDARD DEVIAITON AND COEFFICIENET OF VARIATION

SIZE (Xi) FREQUENCY (Yi) XiYi

12.5 4 50

13.0 19 247

13.5 30 405

14.0 63 882

14.5 66 957

15.0 29 435

15.5 18 279

16.0 1 16

230 3 270

Mean = ∑XiYi/n = 3270/230 = 14.22

Size (Xi) Xi-Mean (Xi-Mean)2

12.5 -1.7 2.89

13.0 -1.2 1.44

13.5 -0.7 0.49

14.0 -0.2 0.04

14.5 0.3 0.09

15.0 0.8 0.64

15.5 1.3 1.69

16.0 1.8 3.24

10.52

VARIANCE =10.52

Standard Deviation= ________________

√ 14.2 X 10.52 = 12.2

Coefficient of variation = standard deviation/mean *100 = 12.2/14.2*100 =86%

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 Production

20 15 15

22 18 17

24 20 20

26 32 18

28 40 20

30 39 21

32 40 15

X Rain fall

TOTAL Production (Y)

(X-X MEAN)2 (y-y mean)2 (x-x mean) (y-y mean)

20 30 36 293.8790 -102.8574

22 35 16 147.4500 -48.5716

24 40 4 51.0210 -42.8574

26 50 0 8.1630 0

28 60 4 165.3050 25.7142

30 60 16 165.3050 51.4284

32 55 36 61.7340 47.1426

∑X=182 ∑Y=330 ∑ (X-X mean)² =112

∑ (Y-Y mean)² =892.857

SUM (X-X mean) (Y-Y mean =70.0012

X mean + 26 Y mean = 47.1429 Sum of squared deviation from rainfall =112 Sum of squared deviation of production =892.857 Sum of cross production = 70.0012 R = -70.0012 = _______________

√ 112 (892.857)

= (70.0012)/316.2277 = 0.2214

INTERPRETATION: The magnitude of the correlation between rainfall and population is =0. 2214. The direction of the relationship is negative. As the rainfall increases the production decreases. 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 28 Marks in Mathematics:30 33 45 23 8 49 12 4 31 Compute their ranks in the two subjects and coefficient of correlation of ranks.

No. Marks in Physics

Rank

Mark in Mathematics

Rank Distance between ranks

D Squared

1 6 9 4 9 0 0

2 9 8 12 7 1 1

3 10 7 8 8 -1 1

4 17 6 23 6 0 0

5 23 5 33 3 2 4

6 28 4 31 4 0 0

7 35 3 30 5 -2 4

8 43 2 49 1 1 1

9 47 1 45 2 -1 1

∑d2=12

(R) = 1-6 ∑d2 N3-n N3-n=729-9=720 R =1-(72/720) =1-0.1 =0.9

Assignment –B

Ques.1 i. Define Binomial, Poisson and Normal distribution.

a. BINOMIAL DISTRIBUTION: It occurs when a random variable X which takes value 0, 1, 2…., n and if its probability functions is given by:

P(X =r) = P(r) =”Cr pʳ qⁿ ˉ ʳ, r = 0, 1,2…..,n, where p, q>0 such that p + q = 1

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 suit

B. POISSON DISTRIBUTION It is generally used when measuring the number of occurrence of something over an interval or time period. The assumptions of a Poisson probability 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

C. NORMAL DISTRIBUTION It is one of the most important and widely used continuous distribution. It has the following characteristics:

It is bell shaped and is systematical about its mean

It is asymptotic to the axis i.e it extend indefinitely in either directions from the mean

It is a continuous distribution

It is family curve

It is unimodal 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 suit

4/13 = 0.31

B. all the four cards of the same number 4/52 = 0.08

C. one card from each suit 4/52 = 0.08

D. two red cards and two black cards 4/52 = 0.08

E. all cards of the same colour

4/26 = 0.15

F. all face cards 4/12 = 0.3

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 82 Productivity index(Y) 68 60 62 80 85 40 52 62 60 81 Calculate the two regression equations and estimate

Worker X1 Y1 X1-X2 Y1-Y2 (X1-X2)2 (Y1-Y2)2 (X1-X2) (Y1-Y2)

1 60 68 -5 3 25 9 -15

2 62 60 -3 5 9 25 -15

3 65 62 0 -3 0 9 0

4 70 80 5 15 25 225 75

5 72 85 7 20 49 400 140

6 48 40 -17 -25 289 625 425

7 53 52 12 -11 144 121 132

8 73 62 8 -3 64 9 -24

9 65 60 0 -5 0 25 0

10 82 81 17 16 289 256 272

650/10 =65

650/1O =65

894 1704 586

By X = ∑xy ∑ x2 =586/894 =0.655481 Y-65=0.655481 X (X-65) Y=0.655481 x22.3937

a. The productivity index of a worker whose test score is 92 PRODUCTIVITY INDEX

Y = 0.655481+22.3937 = 0.655481 x 92 +22.3937 = 89.6980

b. The test score of a worker whose productivity index is 75

TEST SCORE

Y-22.3937= 0.655481X

X=Y-22.3937/0.655481

X=75 – 22.3937/0.0655481

= 80.2560

Ques.3 Discuss the different components of a time series and fit a trend line with the help of following data by using There are four components of a time series according to the text namely

1. Secular Trend – The smooth long term direction of a time series

2. Seasonal Variation – Patterning 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: i. Episodic – unpredictable but identifiable ii. Residual – Also called chance fluctuation and unidentifiable

SECULAR TREND It is said that the value of the variable trend to increase or decrease over a long period of time. SEASONSAL VARIATION It is asserted that this kind of variation involves patterns of change within a year that tends to be repeated from year to year. CYCLICAL VARIATION It is commonly used in the business cycle. There are times when the business cycle hits a peak above the trend line. At times business activity is likely to slump hitting a low point below the trend line. Irregular Variations, it is categorized into the following;

i. Episodic – unpredictable but identifiable

ii. Residual – Also called chance fluctuation and unidentifiable Free hand curve method and Semi-averages method: Year 1993 94 95 96 97 98 99 2000 01 02 03 04 Profit 10 12 16 8 6 14 15 10 14 20 13 18 (Rs. in lakhs)

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

i. Given the form of the scattered diagram, does it appear that a straight line provides an accurate model for the data? Ans. Yes it does because there seems to be a positive correlation between two variables.

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

iii. Find the two lines of regression.

X-(age) Y - Blood Pressure (X-X mean)2

56 147 2578.6084

42 125 1352.7684

36 118 947.4084

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

47 128 1745.5684

49 145 1919.6884

42 140 1352.7684

60 155 30000.8484

72 160 4459.5684

63 149 3338.5284

55 150 2478.0484

∑= 522/10=5.22 ∑= 1417/10+141.7 ∑= 51 173.80/10 =5 117.38

r = . Cov (x, y) . ________

√ (Var x. var y)

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 decisions c. 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 research

b. 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 expression c. empirical observation and social expression

d. empirical observation and all expression√

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

a. Rule of thumb b. Commonsense c. Snap judgment.

d. Quantitative Techniques√

Ques.6 Statistics is a branch of

a. applied physics

b. applied mathematics√

c. applied commerce d. Dramatics

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

a. 14 b. 16 c. 15.4

d. 16.4√

Ques.8 ∑ (X/c) =

a. ∑ ( X)/n c

b. ∑ ( 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. 87,99,75,87,94,75,35,88,87,93 The mode of the distribution

a. 75 b. 87 c. 88

d. 94√

Ques.10 Which measure of Central tendency is most efficient

a. Mean√

b. Median c. Mode

d. All are equal

Ques.11 Mean Deviation can be calculated from

a. Mean√

b. Median c. Mode. d. All the three

Ques.12 Qualitative data are

a. Non-numeric

b. Numeric√

c. Can be both d. None

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

a. Continuous data√

b. Discrete data c. Datum d. 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. Mode√

d. 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. Median

c. Mode√

d. None Ques.17 The correlation coefficient, r = -1, implies

a. Perfect negative√

b. Perfect positive c. No correlation d. 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 positive b. Limited positive c. 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. Both d. 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 relationship c. Perfect negative d. 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 fluctuations d. 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 variable√

c. Random variable d. 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 Y d. the change in Y is exponential

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

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

c. r = +1√

d. r = 0

Ques.27 The regression Analysis Studies

a. one-way causal effect√

b. two-way causal effect c. 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 mean d. 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. 12/30 d. 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. 1/330 c. 9/2500 d. 6/100

Ques.36 Find the correlation coefficient r(X, Y) between X and Y,when

Cov(X,Y) = -2.45, Var (X) = 8.25 and Var (Y) = 21.49

a. 0.18

b. – 0.18√

c. 0.36 d. – 0.36

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

a. 1/2

b. 1/3√

c. 1/4 d. 1/5

Ques.38 Normal Distribution is symmetrical about its

a. Harmonic mean

b. Mean√

c. Range d. 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 +3σ d. 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√