| st. joseph’s college of commerce (autonomous) | |||||||||||||||||||||||||||
| END SEMESTER EXAMINATION – MARCH /APRIL 2015 | |||||||||||||||||||||||||||
| B.Com – IV SEMESTER | |||||||||||||||||||||||||||
| C1 12 402: BUSINESS STATISTICS & RESEARCH TECHNIQUES | |||||||||||||||||||||||||||
| Duration: 3 Hours Max. Marks: 100 | |||||||||||||||||||||||||||
| SECTION – A | |||||||||||||||||||||||||||
| I) | Answer ALL the questions. Each carries 2 marks. (10×2=20) | ||||||||||||||||||||||||||
| 1. | Is there any difference between Statistics and Mathematics? Justify your answer. | ||||||||||||||||||||||||||
| 2. | Raju finds the mean score of 10 batsmen to be 50 and median to be 25. Help him assess the distribution of the scores? | ||||||||||||||||||||||||||
| 3. | Differentiate between Type one and Type two error with a suitable example. | ||||||||||||||||||||||||||
| 4. | Consider a series-0, 12, 13, 15, 67, 90. Find the range and coefficient of range for the series? | ||||||||||||||||||||||||||
| 5. | It is 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against a person now 50 living till he is 80. Find the probability that at least one of these persons would be alive 30 years hence? | ||||||||||||||||||||||||||
| 6. | Coefficient of correlation between two variables X and Y is 0.8. The covariance is 20. The variance is 16? Find the standard deviation of Y series? | ||||||||||||||||||||||||||
| 7. | Differentiate among various Graphs strictly based on dimensions. | ||||||||||||||||||||||||||
| 8. | Explain the reason for taking a factor of 0.6745 while evaluating probable error. | ||||||||||||||||||||||||||
| 9. | The regression coefficient of x on y is 0.5 and y on x is 3.5. Evaluate the correlation coefficient and comment on the regression coefficients. | ||||||||||||||||||||||||||
| 10. | Mention any four problems that need a careful thought before constructing Index numbers. | ||||||||||||||||||||||||||
| SECTION – B | |||||||||||||||||||||||||||
| II) | Answer any FOUR questions. Each carries 5 marks. (4×5=20) | ||||||||||||||||||||||||||
| 11. | From the following marks of 100 students compute the mean deviation from median and its coefficient.
Marks: 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 Students: 6 12 17 28 12 10 8 5 2 |
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| 12. | Construct Fisher’s index number for the following data and prove that it satisfies reversibility tests;
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| 13. | From the following data compute the Regression Coefficients:
X : 8 9 10 10 11 13 14 16 Y : 4 6 8 12 13 15 17 28 |
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| 14. | State the differences between Correlation and Regression. | ||||||||||||||||||||||||||
| 15. | Find the Mean and Median from the following:
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| 16. | Draw Ogives from the following data and measure the median value. Verify it by actual calculations.
Central size : 5 15 25 35 45 Frequency : 5 11 21 16 10
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| SECTION – C | |||||||||||||||||||||||||||
| III) | Answer any THREE questions. Each carries 15 marks. (3×15=45) | ||||||||||||||||||||||||||
| 17. | Amith, Balu and Chandrashekar ranked students. Comment on their compatibility in ranking students :
Amith : 3 5 4 10 8 8 1 6 8 2 Balu : 5.5 5.5 1 8.5 4 10 2 7 8.5 3 Chandrashekar: 9 9 7 5 2 2 2 5 5 9
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| 18. | What do you mean by a questionnaire? State the essential points in drafting a good questionnaire. Make a questionnaire for conducting a study on importance of different facilities available in college. Make a questionnaire for conducting a study on importance of different facilities available in college.
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| 19. | Calculate the trend values for the production figures by least squares method in Alka textile Pvt. Ltd
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20. |
a) A company is engaged in making brake systems for cars. A car running at a speed of 50 kmph comes to a halt after covering a distance of 24 feet on the average when the brake already in use is applied. Recently the company has developed a new brake system which when applied 80 times to cars running at 50 kmph, gave a mean distance of 23.2 feet, with a standard deviation of 2.8 feet, for the cars to come to a halt. Test at 1 percent Level of significance whether the new brake system is superior to the existing one?
b) Mean height of 50 students is 5’-8”. The height of 10 students are given below: 5’-6”, 5’-2”, 5’-4”, 5’-0”, 4’-10”, 4’-8”, 6’-2”,5’-8”, 5’-9”,5’-3”.Find the mean height of remaining students? (10+5) )
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| 21. | a) By using the simultaneous equations method find out the most probable value of y when x=15?
b) The salary for IT managers in state A and state B are shown below: State A: 3.2 4.8 5.3 2.2 2.7 6.2 3.4 3.7 4.1 4.2 5.7 2.5 State B: 1.5 2.6 2.8 4.6 3.6 6.2 6.8 1.3 2.1 1.5 Test at 2% Level of significance whether the difference between mean incomes of two states is equal. (7+8)
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| SECTION – D | |||||||||||||||||||||||||||
| IV) | Case Study (1×15=15) | ||||||||||||||||||||||||||
| 22. | An agent obtained samples of bulbs from the 2 companies. He had them tested for durability and got the following results:
Which company bulbs are uniform?
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