- JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
SUPPLEMENTARY EXAMINATION – APRIL 2013
B.COM. – IV SEMESTER
Business Statistics & reserach techniques
TIME: 3 HRS MARKS : 100
SECTION – A
- I) ANSWER ALL THE QUESTIONS. (10 x 2 = 20)
- Define Business Statistics.
- W hat are Ogives? Which average can be estimated by the help of Ogives ?
- There are two branches of an establishment employing 100 and 80 people respectively. If the arithmetic means of the monthly salaries paid by two branches are Rs 275 and Rs 225 respectively. Find the arithmetic mean of the salaries of the employees of the establishment as a whole.
- What do you understand by the term range? How is it calculated?
- A bag contains 6 white and 4 black balls. One ball is drawn at random. What is the probability that it is white?
- What are the two types of errors in hypothesis testing? Describe them.
- Mention any three methods used for calculation of time series.
- What are Index Numbers?
- Explain the term positive and negative correlation. State in the following cases what type of correlation would you expect: a) shoe size and intelligence b) ages of husbands and wives and c) insurance companies profit and number of claims they have to pay.
- For a sample size 25 from a population, the coefficient of correlation is -0.13. Find the probable error.
SECTION – B
- II) ANSWER ANY FOUR ( 4 X 5 = 20)
- a) What is a pie-diagram?
- b) Construct a pie chart for the following data
Principal Exporting Countries Of Cotton
U.S.A India Egypt Brazil Argentina
6367 2999 1688 650 202.
- The following are the figures of production (in thousand quintals) of a sugar factory
Year 2000 2002 2004 2006 2008 2010 2012
Production 77 81 88 94 94 96 98
- a) fit a straight line trend to the data.
- b) graph the observed values and trend values
- c) estimate the production in the year 2014.
- From the Data given below, calculate Fisher’s Index Number and prove that Fishers Index Number satisfies both Time Reversal Test and Factor Reversal Test.
| Item | Base Year | Current Year | ||
| Price | Quantity | Price | Quantity | |
| M | 5 | 50 | 8 | 40 |
| N | 7 | 25 | 12 | 30 |
| O | 9 | 10 | 15 | 25 |
| P | 12 | 5 | 20 | 18 |
- Explain the meaning and scope of statistics, highlighting its importance particularly in the field of trade and commerce.
- The marks and number of students seen in a class has been observed. Locate the values of the lower quartile, 4th decile and 60th percentile.
Marks Below10 10-20 20-30 30-40 40-50 50-60 60-70 70above
No. Of 13 17 50 60 55 45 23 7
students
- a) A company is to appoint a person as its Managing Director, who must be an M.Com, M.B.A and I.A.S. the probability of which is one in twenty five, one in forty, and one in fifty respectively. Find the probability of getting such a person to be appointed by the Company.
- b) Three groups of children consist of 3 girls and 1 boy, 2 girls and 2 boys and 1 girl and 3 boys. One child is selected at random from each group. Show that the chances that the three selected consist of one girl and two boys is 13/32.
SECTION – C
III) ANSWER ANY THREE QUESTIONS. (3 X 15 =45)
- A) Define Tabulation. What are the different parts of a table?
- B) An investigation conducted by the Education Department in a public library revealed the following facts. You are required to tabulate the information as neatly and clearly as you can:
“in 1950 the total number of the readers was 46,000 and they borrowed some 16,000 volumes. In 1960 the number of books borrowed increased by 4000 and the borrowers by 50%. The classification was on the basis of three sections: Literature, Fiction and Illustrated News. There were 10,000 and 30,000 readers in the sections Literature and Fiction respectively in the year 1950. In the same year, 2,000 and 10,000 books were lent in the sections Illustrated News and Fiction respectively. Marked changes were seen in 1960. There were 7,000 and 42,000 readers in the Literature and Fiction sections respectively. So also 4000 and 13,000 books were lent in the sections Illustrated News and Fiction respectively.”
( 7 + 8)
- a) An automatic machine was designed to pack exactly 2.0 kg of Vanaspati. A sample of 100 tins was examined to test the machine. The average weight was found to be 1.96 kg with S.D of 0.10 kg. Is the machine working properly?
- b) To test the effectiveness of inoculation against cholera the following table were obtained:
| Attacked | Not Attacked | |
| Inoculated | 12 | 28 |
| Not Inoculated | 13 | 7 |
The figures represent the number of persons. Does inoculation prevent attack from cholera?
( 7 + 8)
- In trying to evaluate the effectiveness of its advertising campaign, a firm compiled the following information:
| Year | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 | 1987 |
| Adv. Expenditure(‘000) | 12 | 15 | 15 | 23 | 24 | 38 | 42 | 48 |
| Sale (lakh rs) | 5.0 | 5.6 | 5.8 | 7.0 | 7.2 | 8.8 | 9.2 | 9.5 |
Calculate the regression equation of sales on advertising expenditure. Estimate the probable sales when advertisement expenditure is Rs 60,000.
- The following table gives the figures of profits of two companies X and Y for the last 10 years. Which of the two companies has greater consistency in profits?
| Year | Profits | Year | Profits | ||
| Co. X | Co. Y | Co. X | Co. Y | ||
| 1979 | 700 | 550 | 1984 | 700 | 600 |
| 1980 | 625 | 600 | 1985 | 650 | 550 |
| 1981 | 725 | 575 | 1986 | 700 | 525 |
| 1982 | 625 | 550 | 1987 | 600 | 625 |
| 1982 | 650 | 650 | 1988 | 650 | 600 |
- Write short notes on a) primary and secondary data b) types of frequency distributions
- c) Rank Correlation d) uses of Index numbers e) procedure for testing a hypothesis.
SECTION – D
IV) Compulsory question (1 x 15 =15)
India is the second largest country in the world, with more than a billion people. Nearly three quarters of the people live in rural areas scattered about the countryside in 6,000,000 villages. In fact, it may be said that one in every 10 people in the world live in rural India. Presently the population in India can be described as poor and semi-illiterate. With an annual income of less than 1$ per day, rural India accounts for only about one third of total national product sales.
However, in addition to the impressive size of the population, there are other compelling reasons for companies to market their goods and services to rural India. The market for rural India has been growing at 5 times the rate of urban India. There is increasing agricultural productivity, leading to growth in disposable income, and there is a reduction in the gap between the tastes of urban and rural customers. The literacy level is increasing and people are becoming more conscious about their lifestyles and opportunities for better lives. More than one-third of all rural households have a main source of income other than farming. Virtually every home has a radio, almost 20% have a television, and more than 30% have a bank account.
Toothpaste consumption in India doubled and the consumption of shampoo increased manifold. Other products like bicycles, bath soaps, fans, etc have also done well. Because of such factors, many US and Indian firms, have entered the Indian market. Rural market has a huge untapped market for business. However, entering such a market is not without risks. The dilemma facing the firms is whether to enter this marketplace and if so, to what extent and how.
Questions:
- How and where do you think the researchers could have collected data for this research? Do you think the statistics presented here are exact or estimates?
- What other statistics would help the research become better?
- Formulate a possible null and an alternate hypothesis which can be tested based on the information given above.
- Present the information given above in form of a proper research report.
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