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ADL 07 Quantitative Techniques in Management V3

Assignment – A

Question 1 How has quantitative analysis changed the current scenario in the

management world today?

Question 2 What are sampling techniques? Briefly explain the cluster sampling

technique.

Question 3 What is the significance of Regression Analysis? How does it help a

manager in the decision making process?

Question 4 Explain the following terms in detail (give examples where

necessary): –

a) Arithmetic mean

b) Harmonic mean

c) Geometric mean

d) Median

e) Mode

Question 5 Explain the classical approach to the probability theory. Also

explain the limitation of classical definition of probability.

Assignment – B

Question 1 Write a note on decision making in management. How one will take

decision under risk and uncertainty.

Question 2 The Mumbai Cricket Club, a professional club for the cricketers, has

the player who led the league in batting average for many years. Over the past

ten years, Amod Kambali has achieved a mean batting average of 54.50 runs with a

standard deviation of 5.5 runs. This year Amod played 25 matches and achieved an

average of 48.80 runs only. Amod is negotiating his contract with the club for

the next year, and the salary he will be able to obtain is highly dependent upon

his ability to convince the team’s owner that his batting average this year was

not significantly worse than in the previous years. The selection committee of

the club is willing to use a 0.01 significance level.

You are required to find out whether Amod’s salary will be cut next year.

Question 3 The salaries paid to the managers of a company had a mean of Rs.

20,000 with a standard deviation of Rs 3,000, What will be the mean and standard

deviation if all the salaries are increased by

1) 10%

2) 10% of existing mean

3) Which policy would you recommend if the management does not

want to have increased disparities of wages?

Case Study

Kushal Arora, a second year MBA student, is doing a study of companies going

public for the first time. He is curious to see whether or not there is a

significant relationship between the sizes of the offering (in crores of rupees)

and the price per share after the issue. The data are given below:

Size (in crore of rupees)1083968.405110.404.40

Price (in rupees)121319126.504

Question

You are required to calculate the coefficient of correlation for the above data

set and comment what conclusion Kushal should draw from the sample.

Assignment – C

1.Which of the following is not correct about construction of bar charts?

(a). All bars should rise from the same base line

(b). Width of the bar should be proportional to the data represented

(c). The bars should be arranged from the left to right

(d). Length of the bars should be proportional to the data represented

2.Which of the following is not true about mean absolute deviation :-

(a). Mean deviation is obtained by calculating the absolute deviations of

each observation from mean

(b). Mean deviation is a more comprehensive measure compared to range

(c). It is conducive to further algebraic treatment

(d). It cannot be computed for distributions with open end classes.

3.The value index number measures the–

(a). Changes in prices of a basket of commodities from one period to another

(b). Changes in quantities consumed of a basket of commodities over a period

of time

(c). Change in the total monetary value of a basket of commodities over a

period of time

(d). Change in the retail prices of various commodities

4.A market researcher wants to find out the buying behavior of the typical

household during the weekends. He divides the city into various localities such

that each locality represents the city population in terms of age group, gender

and social status. Then he randomly selects five localities and surveys each

household. Which of the following sampling techniques best describes the method

used by the researcher :-

(a). Cluster sampling

(b). Systematic sampling

(c). Stratified sampling

(d). Convenience sampling.

5. If every item in the data set is increased by the same quantity then the

standard deviation of the data set–

(a) Remains the same

(b) Increases by the same quantity by which every data item is increased

(c) Decreases by the same quantity by which every data item is increased

(d) Increases by the square root of the same quantity by which every data

item is increased

6. Which of the following is true with regard to a linear equation Y – a – bX =

0, where X is the independent variable and Y is the dependent variable :-

(a) The slope of the straight line is ‘a’

(b) The Y-intercept of the straight line is 0

(c) The Y-intercept of the straight line is ‘b’

(d) The slope and the Y-intercept remain constant for all combinations of X

and Y values which satisfy the equation

7. Which of the following quantitative method is not used by managers to take

decision :-

(a) Linear programming

(b) Time series

(c) Regression analysis

(d) Hypothesis testing

8. In the graphical method of solving linear programming problems the feasible

region is the set of all points–

(a) Which does not satisfy any of the constraints?

(b) Which satisfy exactly one of the constraints?

(c) Which satisfy all the constraints?

(d) At which the objective function has the same value?

9. Which of the following is false in regard to histogram :-

(a) The class intervals are represented by the base of the rectangles

(b) The frequencies are represented by the heights of the rectangle

(c) If the class intervals are of equal width then the bases of the

rectangles will be equal in length

(d) The tallest rectangle in a histogram represents the class interval with

the lowest frequency

10. Which of the following measures in not affected by the presence of extreme

values in a dataset :-

(a) Range

(b) Arithmetic mean

(c) Standard deviation

(d) Median

11. 12x + 1/3y – 1/3z = -1

1/3x – 1/2y -1/6z = 4

1/6x – 5/6y + 1/2z = 3

The values of x in the above simultaneous equations would be–

(a) 3

(b) 6

(c) 9

(d) 12

12. The following details are available with regard to a data set: Sx = 33, Sx2

= 199,

n = 6. If each observation in the data set is multiplied by 2 then the standard

deviation of the resulting values will be equal to:

(a) (35/3)1/2

(b) 35/3

(c) 3

(d) 25

13. The following data pertains to three commodities :-

Commodity Price in 2004 (Rs. /kg) Price in 1994 (Rs. /kg)

Rice

Wheat

Pulses 11.50

13.50

26 9.50

8.50

20

The base year is 1994. The unweighted aggregates price index for the year 2004

is approximately–

(a) 115.62

(b) 125.45

(c) 134.21

(d) 250.55

14. If the regression equation is the perfect estimator of the dependent

variable then which of the following is false?

(a) The standard error of estimate is zero

(b) The coefficient of correlation is zero

(c) The coefficient of determination is 1.00

(d) All the data points fall on the regression line

15. If the regression equation is a perfect estimator of the dependent variable

then which of the following is false :-

(a) The standard error of estimate is zero

(b) The coefficient of correlation is zero

(c) The coefficient of determination is 1.00

(d) All the data points fall on the regression line

16. Which of the following represents the proportion of variation in the

dependent variable that is explained by the regression line :-

(a) Coefficient of determination

(b) Coefficient of correlation

(c) Coefficient of variation

(d) Standard error of estimate

17. If the coefficient of correlation between the two variables lies between -1

and 0, then the covariance between them is–

(a) Positive

(b) Negative

(c) Zero

(d) Equal in magnitude to the variances of both the variables

18. If bYX is the slope of coefficient of regression line of Y on X, and bXY is

the slope coefficient of regression line of X on Y then which of the following

is true :-

(a) bYX is positive implies that bXY is positive

(b) bYX is positive implies that bXY is negative

(c) bYX and bXY are reciprocals

(d) The product of bYX and bXY is zero

19. A graphical method of representing states of nature and courses of action

involved in decision making is referred to as–

(a) Decision tree

(b) Histogram

(c) Scatter diagram

(d) Frequency distribution

20. If the probability of occurrence of one event is not affected by the

occurrence of another event and vice versa then the two events are said to be–

(a) Collectively exhaustive

(b) Independent

(c) Dependent

(d) Mutually exclusive

21. Bayes’ theorem helps the statistician to calculate—

(a) Dispersion

(b) Subjective probability

(c) Posterior probability

(d) Classical probability

22. In a binomial distribution the probability of getting zero or more numbers

of successes is equal to–

(a) 0

(b) 1

(c) The probability of getting zero success

(d) The probability of getting successes in all trials

23. Which of the following measures represent the scatter of the values in a

data set :-

(a) Arithmetic mean

(b) Geometric mean

(c) Standard deviation

(d) Median

24. As the sample size increases–

(a) The variation of the sample mean from the population mean becomes larger

(b) The variation of the sample mean from the population mean becomes smaller

(c) The variance of the sample becomes less than the variance of the

population

(d) The standard deviation of the sample becomes more than the standard

deviation of the population.

25. In the graphical method of solving linear programming problems if there is a

unique optimal solution, then the optimal solution–

(a) Is always found at the center of the feasible region

(b) Is always at the origin

(c) Lies outside the feasible region

(d) Is located at one of the corner points of the feasible region

26. A multiple regression equation has–

(a) Multiple dependent variables

(b) One independent variable

(c) One dependent variable

(d) A standard error of estimate equal to zero

27. Which of the following conditions indicate the existence of multiple optimal

solutions when a linear programming problem is solved by the graphical method :-

(a) One of the constraints is parallel to the horizontal axis

(b) The objective function is parallel to the vertical axis

(c) The objective function is parallel to one of the edges of the feasible

region which is in the direction of optimal movement of the objective function

(d) If two or more constraints are parallel to each other

28 Three persons enter into a railway carriage and there are 8 seats available.

In how many ways they can seat themselves?

(a) 24

(b) 336

(c) 40

(d) 56

29. In which of the following the simple harmonics mean is appropriate :-

(a) A set of ratios using the numerators of the ratio data as weights

(b) A set of ratios using the denominators of the ratio data as weights

(c) A set of ratios which have been calculated with the same numerators

(d) A set of ratios which have been calculated with the same denominators

30. Which of the following statements is not true about standard deviation?

(a) Combined standard deviation of two or more groups can be calculated

(b) The sum of the squares of the deviations of items of any series from a

value other than the arithmetic mean would always be smaller

(c) Standard deviation is independent of any change of origin

(d) Standard deviation is dependent on the change of scale

31. Which of the following is/are true with respect to geometric mean :-

(a) Geometric mean cannot be calculated if any of the value in the set is

zero.

(b) Geometric mean is appropriate for averaging the ratios of change, for

average of proportions, etc.

(c) Geometric mean is considered most suitable average for index numbers.

(i) Only (I) above

(ii) Only (II) above

(iii) All (I), (II) and (III) above

(iv) Only (II) above

32. The probability of getting two heads from three tosses of a fair coin is–

(a) 1/8

(b) 1/4

(c) 3/8

(d) 1/2

33. If A and B are two mutually exclusive events and P(A) = 2/3, then the

probability of events A and B happening together is–

(a) 0

(b) 1/3

(c) 2/3

(d) 1/2

34. Which of the following can be directly used as the test statistic in

hypothesis tests on the basis of non standardized scale :-

(a) The sample mean, when the test involves the population mean.

(b) The difference between two sample means, when the tests involve the

difference between two population means.

(c) The sample proportion when the test is about the population proportion

(i) Only (a) above

(ii) Only (b) above

(iii) Only (c) above

(iv) All (a), (b), (c) above

35. A box contains 60 ball point pens out of which 10 pens are defective. 8 pens

are randomly picked up from the box. The probability distribution of the number

of pens which are randomly picked, will be–

(a) A discrete uniform distribution

(b) A binomial distribution

(c) A hyper geometric distribution

(d) A Chi- square distribution

36. If we consider the process of selecting a simple random sample as an

experiment then which of the following can be treated as random variable(s)?

(a) Sample mean

(b) Sample standard deviation

(c) Sample range

(d) Sample median

(i) Only (a) above

(ii) Only (b) above

(iii) All (a), (b), (c), (d) above

(iv) Only (d) above

37. The covariance of random variable with itself is always–

(a) A positive quantity

(b) A negative quantity

(c) 0

(d) Less than its expected value

38. A man has 6 friends. In how many ways he can invite one or more of them to a

party?

(a) 63

(b) 64

(c) 119

(d) 120

39. Find x; if logx/log2 = log36/log4

(a) 0

(b) 2

(c) 4

(d) 6

40. The empirical relationship between range (R) and mean deviation (M.D) is–

(a) 2R=15M.D

(b) 3R=17M.D

(c) R=17M.D

(d) 3R=M.D

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