Quantitative Techniques in Management-2

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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) 108 39 68.40 51 10.40 4.40
Price (in rupees) 12 13 19 12 6.50 4

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. A survey to collect data on the entire population is

a)   a census

b)   a sample

c)   a population

d)   an inference

 

2. A portion of the population selected to represent the population is called

a)   statistical inference

b)   descriptive statistics

c)   a census

d)   a sample

 

3. Qualitative data can be graphically represented by using a(n)

a)   histogram

b)   frequency polygon

c)   ogive

d)   bar graph

4. Fifteen percent of the students in a school of Business Administration are majoring in Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical device(s) which can be used to present these data is (are)

a)   a line graph

b)   only a bar graph

c)   only a pie chart

d)   both a bar graph and a pie chart

 

5. A histogram is

a)   a graphical presentation of a frequency or relative frequency distribution

b)   a graphical method of presenting a cumulative frequency or a cumulative relative frequency distribution

c)   the history of data elements

d)   the same as a pie chart

 

6. The mean of a sample

a)   is always equal to the mean of the population

b)   is always smaller than the mean of the population

c)   is computed by summing the data values and dividing the sum by (n – 1)

d)   is computed by summing all the data values and dividing the sum by the number of items

 

7. The median of a sample will always equal the

a)   mode

b)   mean

c)   50th percentile

d)   all of the above answers are correct

 

8. The difference between the largest and the smallest data values is the

a)   variance

b)   interquartile range

c)   range

d)   coefficient of variation

 

9. The most frequently occurring value of a data set is called the

a)   range

b)   mode

c)   mean

d)   median

 

10. The heights (in inches) of 25 individuals were recorded and the following statistics were calculated

mean = 70 range = 20

mode = 73 variance = 784

median = 74

The coefficient of variation equals

a)   11.2%

b)   1120%

c)   0.4%

d)   40%

 

11. The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals

a)   8

b)   10

c)   6400

d)   4,096

 

12. Which of the following is not a measure of dispersion?

a)   the range

b)   the 50th percentile

c)   the standard deviation

d)   the interquartile range

 

13. The coefficient of variation is

a)   the same as the variance

b)   the standard deviation divided by the mean times 100

c)   the square of the standard deviation

d)   the mean divided by the standard deviation

 

14. A numerical measure of linear association between two variables is the

a)   variance

b)   coefficient of variation

c)   correlation coefficient

d)   standard deviation

 

15. The coefficient of correlation ranges between

a)   0 and 1

b)   -1 and +1

c)   minus infinity and plus infinity

d)   1 and 100

 

16. The model developed from sample data that has the form of y =b0 + b1x is known as

a)   regression equation

b)   correlation equation

c)   estimated regression equation

d)   regression model

 

17. A Regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation

Y = 30,000 + 4X

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

 

18. Regression analysis is a statistical procedure for developing a mathematical equation that describes how

a)   one independent and one or more dependent variables are related

b)   several independent and several dependent variables are related

c)   one dependent and one or more independent variables are related

d)   None of these alternatives is correct

 

19. Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the following estimated regression equation was obtained

Ỹ=120-10x

Based on the above estimated regression equation, if price is increased by 2 units than demand is expected to?

a)   increase by 120 units

b)   increase by 100 units

c)   increase by 20 units

d)   decease by 20 units

 

20. Which of the following is not present in a time series?

a)   seasonality

b)   operational variations

c)   trend

d)   cycles

 

21. The trend component is easy to identify by using

a)   moving averages

b)   exponential smoothing

c)   regression analysis

d)   the Delphi approach

 

22. The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effect is

a)   moving averages

b)   mean squared error

c)   mean average deviation

d)   qualitative forecasting methods

 

23. If P(A) = 0.4, P(B | A) = 0.35, P(A  U B) = 0.69, then P(B) =

a)   0.14

b)   0.43

c)   0.75

d)   0.59

 

24. If P(A) = 0.5 and P(B) = 0.5, then P(A  ∩ B)

a)   is 0.00

b)   is 1.00

c)   is 0.5

d)   None of these alternatives is correct.

 

25. A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a

a)   uniform probability distribution

b)   binomial probability distribution

c)   hypergeometric probability distribution

d)   normal probability distribution

 

26. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

a)   0.2592

b)   0.0142

c)   0.9588

d)   0.7408

 

27. The center of a normal curve is

a)   always equal to zero

b)   is the mean of the distribution

c)   cannot be negative

d)   is the standard deviation

 

28. Given that Z is a standard normal random variable, what is the probability that -2.08 ≤ Z ≤ 1.46?

a)   0.9091

b)   0.4812

c)   0.4279

d)   0.0533

 

29. A tabular representation of the payoffs for a decision problem is a

a)   decision tree

b)   payoff table

c)   matrix

d)   sequential matrix

 

30. A decision criterion which weights the payoff for each decision by its probability of occurrence is known as the

a)   Payoff criterion

b)   expected value criterion

c)   probability

d)   expected value of perfect information

 

31. The expected opportunity loss of the best decision alternative is the

a)   expected monetary value

b)   payoff

c)   expected value of perfect information

d)   None of these alternatives is correct.

 

32. An assumption made about the value of a population parameter is called a

a)   hypothesis

b)   conclusion

c)   confidence

d)   significance

 

33. The level of significance is the

a)   maximum allowable probability of Type II error

b)   maximum allowable probability of Type I error

c)   same as the confidence coefficient

d)   same as the p-value

 

34. The level of significance in hypothesis testing is the probability of

a)   accepting a true null hypothesis

b)   accepting a false null hypothesis

c)   rejecting a true null hypothesis

d)   None of these alternatives is correct.

 

35. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

a)

b)

c)    (Correct Option C)

d)

 

36. Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in

a)   bounded form.

b)   feasible form.

c)   standard form.

d)   alternative form.

 

37. If an artificial variable is present in the ‘basic variable’ column of simplex table, then the solution is

a)   degenerate

b)   infeasible

c)   unbounded

d)   none of the above

 

38. The solution to a transportation problem with m-row and n-columns is feasible if number of positive allocations are:

a)   m x n

b)   m + n

c)   m + n – 1

d)   m + n + 1

 

39. Slack

a)   is the difference between the left and right sides of a constraint.

b)   is the amount by which the left side of a ≥ constraint is larger than the right side.

c)   exists for each variable in a linear programming problem.

d)   is the amount by which the left side of a ≤ constraint is smaller than the right side.

 

40. To find the optimal solution to a linear programming problem using the graphical method

a)   find the feasible point that is at the highest location.

b)   find the feasible point that is closest to the origin.

c)   find the feasible point that is the farthest away from the origin.

d)   None of the alternatives is correct.