Few Web Questions.docx

Q16. The weekly wages of 1000 workers are normally distributed around a mean of Rs. 70 and a standard deviation of Rs. 5. Estimate the number of workers whose weekly wages will be: 1. Between 70 and 72 2. Between 69 and 72 3. More than 75 4. Less than 63 Q17. 1. Explain the characteristics of Statistics. 2. What are the components of Statistics? Give a brief description of each of the components. Q18. Explain the objectives of Statistical Average. What are the requisites of a good average? Q19. a. Mention the Characteristics of Chi-square test. 1. Two research workers classified some people in income groups on the basis of sampling studies. Their results are as follow: Income groups Investigators

Poor

Middle

Rich

Total

A

160

30

10

200

B

140

120

40

300

Total

300

150

50

500

Show that the sampling technique of atleast one research worker is defective. Q20. Define trend. Enumerate the methods of determining trend in time series Q21. Explain Chi-square test and the conditions for applying chi-square test Q22. The following data represent the number of units of production per day turned out by 5 different workmen using different types of machines. 10 marks Machine Type Workmen

A

B

C

D

1

44

38

47

36

2

46

40

52

43

3

34

36

44

32

4

43

38

46

33

5

38

42

49

39

i) Test whether the mean productivity is the same for the four different machine types. ii) Test whether 5 men differ with respect to mean productivity. Q23. a) The procedure of testing hypothesis requires a researcher to adopt several steps. Describe in brief all such steps. b) Explain the Components of time series. Q24. Distinguish between Classification and Tabulation. Explain the structure and components of a Table with an example.

Q25. a) Describe the characteristics of Normal probability distribution. b) In a sample of 120 workers in a factory, the mean and standard deviation of wages were Rs. 11.35 and Rs.3.03 respectively. Find the percentage of workers getting wages between Rs.9 and Rs.17 in the whole factory assuming that the wages are normally distributed. Q26. b) Distinguish between: 1. Stratified random sampling and Systematic sampling 2. Judgement sampling and Convenience sampling 3. Judgement sampling and Convenience sampling Q27. a) What is regression analysis? How does it differ from correlation analysis? b) Calculate Karl Pearson’s coefficient of correlation between X series and Y series. X

110

120

130

120

140

135

155

160

165

1

Y

12

18

20

15

25

30

35

20

25

1

Q28. Briefly explain the methods and theories of Business forecasting. Q29. Construct Fisher’s Ideal Index for the given information and check whether Fisher’s formula satisfies Time Reversal and Factor Reversal Tests. Items

P0

Q0

P1

Q1

A

16

5

20

6

B

12

10

18

12

C

14

8

16

10

D

20

6

22

10

E

80

3

90

5

F

40

2

50

5

Q30. Define “Statistics” What are the functions of Statistics? Distinguish between Primary data and Secondary data Q31. Find the (i) arithmetic mean and (ii) the median value of the following set of values: 40, 32, 24, 36, 42, 18, 10. Q32. Explain the following terms with respect to Statistics: (i) Sample, (ii) Variable, (iii) Population. Q33. An unbiased coin is tossed six times. What is the probability that the tosses will result in: (i) exactly two heads and (ii) at least five heads. Q34. Find the median value of the following set of values: 45, 32, 31, 46, 40, 28, 27, 37, 36, 41. Q35. Explain briefly the types of sampling Q36. What are the types of classification of data? Q37. Find the (i) arithmetic mean and (ii) range of the following data: 15, 17, 22, 21, 19, 26, 20. Q38. Suppose two houses in a thousand catch fire in a year and there are 2000 houses in a village. What is the probability that: (i) none of the houses catch fire and (ii) At least one house catch fire?

Q39. Find Karl Pearson’s correlation coefficient between the sales and expenses from the data given below: Sales (Rs. Lakhs)

50

50

55

60

65

65

65

60

60

Expenses (Rs. Lakhs)

11

13

14

16

16

15

15

14

13

Q40. The incidence of occupational disease in an industry is such that the workers have a 20% chance of suffering from it. What is the probability that out of six workers 4 or more will contract the disease? Q41. Construct index numbers of price for the following data by applying: i) Laspeyre’s method ii) Paasche’s method iii) Fisher’s Ideal Index number Base year

Current year

Commodity

Price

Quantity

Price

Quantity

A

2

8

4

6

B

5

10

6

5

C

4

14

5

10

D

2

19

2

13

Q42. Find Karl Pearson’s correlation co-efficient for the data given in the below table: X

18

16

12

8

4

Y

22

14

12

10

8

Q43. Find the (i) arithmetic mean (ii) range and (iii) median of the following data: 15, 17, 22, 21, 19, 26, 20. Q44. (a) Explain Arithmetic mean. (b) The mean wage is Rs. 75 per day, SD wage is Rs. 5 per day for a group of 1000 workers and the same is Rs. 60 and Rs. 4.5 for the other group of 1500 workers. Find the mean and standard deviation for the entire group. Q45. Mr. Arun and Mr. Bhandari play a game. If Mr. Arun picks up an even number from 1 to 6, Mr. Bhandari will pay him double the amount equal to picked up number. If Mr. Arun picks up an odd number then he has to pay amount equal to double the picked up number. What is Mr. Arun’s expectation? Q46. The probability that an employee will get an occupational disease is 20%. In a firm having five employees, what is the probability that: i) None of the employees get the disease ii) Exactly two will get the disease iii) More than four will contract the disease Q47. Microsoft estimated that out of 10,000 potential software buyers, 35% wait to purchase the new OS Windows Vista, until an upgrade has been released. After an advertising campaign to reassure the public was released, Microsoft surveyed 3000 buyers and found 950 who are

still skeptical. At 5% level of significance, can the company conclude that the population of skeptical people had decreased?