Business Statistics-2A

Business Statistics

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Q1: Public transportation and the automobiles are two options an employee can use to get to work each day. Samples of time (in minutes) recorded for each option are shown below

Public transportation	28	29	32	37	33	25	29	32	41	34
Automobile	29	31	33	32	34	30	31	32	35	33

(a) Compute the sample mean time to get to work for each option.

(b) Compute the sample standard deviation for each option.

(c) Which method of transportation is more consistent?

 

Q2: A record was kept over a period of 6 months by a sales manager to determine the average number of calls made per day by his six salesmen. The results are shown below:

Salesman	A	B	C	D	E	F
Average number of calls per day	8	10	12	15	7	5

(a) Compute a measure of skewness. Is the distribution symmetrical?

(b) Compute a measure of kurtosis. What does this measure mean?

 

Q3: The HRD manager of a company wants to find a measure which he can use to fix the monthly income of persons applying for a job in the production department. As an experimental project, he collected data on 7 persons from that department referring to years of service and their monthly income.

Years of service	11	7	9	5	8	6	10
Income (Rs. In 1000’s)	10	8	6	5	9	7	11

(a) What is the degree of association (correlation) between years of service and income?

(b) Find the regression equation of income on years of service.

(c) What initial start would you recommend for a person applying for the job having served in a similar capacity in another company for 13 years?

 

Q4: In 2003 a firm began downsizing in order to reduce its costs. One of the results of these cost cutting measures has been a decline in the percentage of private industry jobs that are managerial. The following data show the percentage of females who are managers from 2003 to 2010.

Years	2003	2004	2005	2006	2007	2008	2009	2010
Percentage	6.7	5.3	4.3	6.1	5.6	7.9	5.8	6.1

(a) Develop a linear trend for this time series.

(b) Use this trend to estimate the percentage of females who are managers in 2011.

 

Q5: Answer any three of the following

1. a) Define Statistics. What are the important functions and limitations of Statistics?
2. b) What is the difference between primary and secondary data? Give different methods of collecting them.
3. c) What are the various types of correlation?
4. d) What are the various components of a time series?
5. e) Explain scatter diagram method of determining correlation.

 

Q6: A departmental store has been the target of many shoplifters during the past month, but owing to increased security precautions, 250 shoplifters have been caught. Each shoplifter’s sex is noted, also noted is whether he/she was a first time or repeat offender. The data are summarized in the table below:

Sex	First time offenders	Repeat offender
Male	60	70
Female	44	76

Assuming that an apprehend shoplifter is chosen at random, find:

(a) The probability that the shoplifter is male.

(b) The probability that the shoplifter is a first time offender, given that the shoplifter is male.

(c) The probability that the shoplifter is female, given that the shoplifter is a repeat offender.

(d) The probability that the shoplifter is female, given that the shoplifter is a first time offender.

 

Q7: Explain the various types of sampling methods. The manager of a courier service believes that packets delivered at the end of the month are heavier than those delivered early in the month. As an experiment, he weighed a random sample of 20 packets at the begigning of the month. He found that the mean weight was 5.25 kgs with a standard deviation of 1.20 kgs. Ten packets randomly selected at the end of the month had a mean weight of 4.96 kgs and a standard deviation 1.15 kgs. At the 0.05 significance level, can it be concluded that the packets delivered at the end of the month weigh more?

 

Q8: A manufacturer produces two different models: X and Y, of the same product. Model X makes a contribution of Rs. 50 per unit and model Y, Rs. 30 per unit towards total profit. Raw materials R1 and R2 are required for production. Atleast 18 kg of R1 and 12 kg of R2 must be used daily. Also atmost 34 hours of labour are to be utilized. A quantity of 2 kg of R1 is needed for model X and 1 kg of R1 for model Y. For each of X and Y, 1 kg of R2is required. It takes 3 hours to manufacture model X and 2 hours to manufacture model Y. How many units of each model should be produced to maximize the profit?(Use graphical method to solve).

 

 

Case Study

 

ACC – A pioneer in the Indian cement industry

 

Associated Cement Companies Ltd. (ACC) came into existence in 1936, after the merger of 10 companies belonging to four important business groups: Tatas, Khataus, Killick Nixon, and F E Dinshaw. The Tata group was associated with ACC since its inception. It sold 14.45% of its share to Gujrat Ambuja cements Ltd between 1999 and 2000. After this strategic alliance, Gujrat Ambuja Cements Ltd became the largest single stakeholder in ACC. In 2005, ACC entered into a strategic relationship with the Holcim group of Switzerland, a world leader in cement as well as a large supplier of concrete, aggregates, and certain construction related services. These global strategic alliances have strengthened the company.

 

ACC is India’s foremost manufacturer of cement and concrete. The company has a wide range of operations with 14 modern cement factories, more than 30 ready mix concrete plants, 20 sales offices, and seven zonal offices. ACC’s research and development facility has a unique track record of innovative research, product development, and specialized consultancy services. ACC’s brand name is synonymous with cement and it enjoys a high level of equity in the Indian market.

 

The Impact of Cartelization

Cartelization is one of the major problems in the cement industry. Cartelization takes place when dominant players of the industry join together to control prices and limit competition. In the Indian market, manufacturers have been known to enter into agreements to artificially limit the supply of cement so that the price remains high. When markets are not sufficiently regulated, large companies may be tempted to collude instead of competing with each other. For example, in May 2006, the competition Council of Romania imposed a combined fine of 27 million Euros on France’s Lafarge, Switzerland’s Holcim, and Germany’s Carpatcement for being involved in the cement cartel in the Romanian market. These three companies share 98% of Romanian cement capacity. The government shouls appropriate actions to check acts of cartelization.

 

Escalating input and fuel costs have forced manufacturers to tap new sources of supply and increase the quest for alternative fuels and raw materials. The cement industry is faced with the challenge of optimizing the utilization of scare basic raw materials and fossil fuels while simultaneously protecting the environment and maintaining emission levels within acceptable limits. It is vital for the cement industry to achieve high levels of energy utilization efficiencies and to sustain them continuously. Table below exhibits sales turnover and advertisement expenses of ACC from 1995 to 2007.

 

Year       Sales (in million rupees)                Advertisement (in million rupees)

1995 20,427 58

1996 23,294 72

1997 24,510 122

1998 23,731 61

1999 25,858 144

2000 26,792 132

2001 29,361 172

2002 32,260 184

2003 33,718 259

2004 39,003 334

2005 45,498 321

2006 37,235 336

2007 64,680 442

 

Q1: Develop an appropriate regression model to predict sales from advertisement

Q2: Calculate the coefficient of correlation and state its interpretation.

Q3. Predict the sales when advertisement is Rs. 500 million.

Section – C

1. The algebraic sum of the deviations from mean is:

1. Maximum
2. Minimum
3. Zero
4. None of the above

2. The arithmetic mean of the first n natural numbers 1, 2, ……,n is:

1. n/2
2. (n+1)/2
3. n(n+1)/2
4. None of the above

3. Which of the following relationship is true for a asymmetrical distribution:

1. mean – mode = 3(mean – median)
2. mode = 3medain – 2mean
3. 3medain = 2mean + mode
4. All of the above

4. If the mean and coefficient of variation of a set of data is 10 and 5 respectively, then the standard deviation is:

1. 10
2. 50
3. 5
4. None of the above

5. If the first and third quartiles are 22.16 and 56.36 respectively, then the quartile deviation is:

17. 1
18. 2
19. 3
20. None of the above

6. The relationship between mean deviation and quartile deviation is:

1. MD = 5/6 QD
2. MD = 6/5 QD
3. MD = 4/5 QD
4. MD = 5/4 QD

7. If the mean deviation is 8, then the value of the standard deviation will be:

 

1. 15
2. 12
3. 10
4. None of the above

8. If quartile deviation is 8, then the value of standard deviation will be:

 

1. 12
2. 16
3. 24
4. None of the above

 

9. If events are mutually exclusive, then:

 

Options

1. their probabilities are less than one
2. their probabilities sum to one
3. both events cannot occur at the same time
4. both of them contain every possible outcome of an experiment.

 

10. Posterior probabilities for certain events are equal to their prior probabilities provided:

Options

1. all the prior probabilities are less than zero.
2. Events are mutually exclusive
3. Events are statistically independent
4. None of the above

 

11. What is the probability that a value chosen at random from a population is larger than the median of the population?

 

Options

1. 25
2. 50
3. 75
4. 1

 

12. Bayes’ theorem is useful in

 

Options

1. Revising probability estimates
2. Computing conditional probabilities
3. Computing sequential probabilities
4. None of the above
5. A probability of getting the digit 2 in a throw of unbiased dice is

 

Options

1. 0
2. ½
3. 1/6
4. ¾

 

14. A bag contains 3 red, 6 white and 7 blue balls. If two balls are drawn at random, then the probability of getting both white balls is

 

Options

1. 5/40
2. 6/40
3. 7/40
4. 14/40

 

15. What is the probability of getting more than 4 in rolling a dice?

 

Options

1. 1/6
2. 1/3
3. ½
4. 1

 

If the outcome is an odd number when a die is rolled, then the probability that it is a prime number is

 

16. Options
17. 1/3
18. 2/3
19. 1/6
20. 5/6

 

 

 

Options

1. Independent
2. Dependent
3. Equally likely
4. None of the above

 

 

18.

 

Options

1. 10
2. 90
3. 00
4. 75

 

19. In a binomial distribution if n is fixed and p > 0.5, then

 

Options

1. The distribution will be skewed to left
2. The distribution will be skewed to right
3. The distribution will be symmetric
4. Cannot say anything

 

20. The binomial distribution is symmetric when

Options

1. p < 0.5
2. p > 0.5
3. p = 0.5
4. p has any value

 

21. The standard deviation of the binomial distribution is:

 

Options

1. np
2. √np
3. npq
4. √npq

 

22. All normal distribution are

 

Options

1. Bell shaped
2. Symmetrical
3. Defined by its parameter
4. All of the above

 

Options

1. 2
2. 5
3. 10
4. 15

 

24. For a standard normal probability distribution, the mean µ and standard deviation are:

 

Options

1. µ = 0 , s = 1
2. µ = 16 , s = 4
3. µ = 25 , s = 5
4. µ = 100 , s = 10

 

25. For a normal distribution if mean is 30, then its mode value is

 

Options

1. 15
2. 30
3. 50
4. None of the above

 

26. Which of the following is a necessary condition for using a t distribution?

 

Options

1. Small sample size
2. Unknown population standard deviation
3. Both (a) and (b)
4. Infinite population

 

27. Sampling distribution is usually the distribution of

 

Options

1. Parameter
2. Statistic
3. Mean
4. Variance

 

28. The process of selecting a subset of a population for a survey is known as

 

Options

1. Survey research
2. Representation
3. Triangulation
4. Sampling

 

29. What is sampling for groups with considerable variation but similar to each other called?

Options

1. Cluster
2. Stratified
3. Systematic
4. Random

 

30. If the relationship between x and y is positive, as variable y decreases, variable x

 

Options

1. Increases
2. Decreases
3. Remains same
4. Changes linearly
5. The line of best fit to measure the variation of observed value of dependent variable in the sample data is

 

Options

1. Regression line
2. Correlation coefficient
3. Standard error
4. None of these

 

Options

1. Less than one
2. More than one
3. Equal to one
4. None of these

 

33. Linear programming is a

 

Options

1. Constrained optimization technique
2. Technique for economic allocation of limited resources
3. Mathematical technique
4. All of the above Solution by DistPub – Amity Solved Assignments

 

34. A constraint in a linear programming model restricts

 

Options

1. Value of objective function
2. Value of a decision variable
3. Use of the available resources
4. All of the above – Solution by DistPub – Amity Solved Assignments

 

35. The best use of linear programming technique is to find an optimal use of

 

Options

1. Money
2. Manpower
3. Machine
4. All of the above

 

36. While solving a LP model graphically, the area bounded by the constraints is called

 

Options

1. Feasible region
2. Infeasible region
3. Unbounded solution
4. Unbounded solution

 

37. A feasible solution to an LP problem

 

Options

1. Must satisfy all the problem’s constraints simultaneously
2. Need not satisfy all the constraints, only some of them
3. Must be a corner point of the feasible region
4. Must optimize the value of the objective function

 

38. The standard deviation of first n natural numbers is:

 

 

39. Two events A and B are statistically independent when

 

40. For a standard normal probability distribution, the mean µ and standard deviation are

 

Options

 

1. µ = 0 ,  σ = 1
2. µ = 16 ,  σ = 4
3. µ = 25 ,  σ = 5
4. µ = 100 ,  σ = 10