Quantitative Applications in Management and Research-1

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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.

 

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

 

 

  1. Form a frequency distribution having 9 class intervals
  2. Form a percentage distribution from the frequency distribution (from part a)
  3. Form a histogram, frequency polygon and frequency curve of the frequency distribution (from part a)

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

 

Size Frequency
12.513.0

13.5

14.0

14.5

15.0

15.5

16.0

419

30

63

66

29

18

1

 

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

 

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.

 

Assignment -B

Ques.1:

i. Define Binomial, Poisson and 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 suit

b. all the four cards of the same number

c. one card from each suit

d. two red cards and two black cards

e. all cards of the same colour

f. all face cards

 

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

  1. The productivity index of a worker whose test score is 92
  2. The test score of a worker whose productivity index is 75

 

 

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 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)

  1. Given the form of the scattered diagram, does it appear that a straight line provides an accurate model for the data?
  2. Find the correlation coefficient between Age(X) and Blood Pressure(Y) and discuss its nature.
  3. Find the two lines of regression.
  4. Estimate the blood pressure of a woman whose age is 45

 

 

 

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

  1. Static decision
  2. Where uncertainly exists
  3. Nature is opponent.
  4. All of above

 

Ques.3 Quantitative analysis is also called

  1. Operations research
  2. Management science
  3. Quantitative techniques
  4. 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

  1. 14
  2. 16
  3. 15.4
  4. 16.4

 

Ques.8 ? (X/c) =

  1. ? ( X)/n c
  2. ? ( X)/? c
  3. ? ( X)/c
  4. 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

e.

 

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

  1. CV = .S . X 100

Xmean

 

  1. CV = .S .

Xmean

 

  1. CV = . Xmean . X 100

S

 

  1. CV = (X – Xmean )

 

 

 

Ques.15: Which one is unaffected by extreme scores

  1. Mean
  2. Median
  3. Mode
  4. 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:

  1. trend
  2. seasonal variation
  3. irregular fluctuations
  4. a cycle

 

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

  1. All trials must be identical.
  2. All trials must be independent.
  3. Each trial must be classified as a success or a failure.
  4. 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:

  1. the change in Y is an additive constant.
  2. the change in Y is a constant for each unit change in X
  3. the change in Y is a fixed percent of Y
  4. 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.

 

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

prob_q1b

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 atleast 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 – s and µ +s

b. µ – 2s and µ +2s

c. µ – 3s and µ +3s

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