STATISTICS FOR MANAGEMENT

MB0024

MBA-I

STATISTICS FOR MANAGEMENT

SAMPLE PAPER

1. A study of characteristics of units of a population by using statistical device and techniques is called:

1. Statistical Investigation
2. Statistical Survey
3. Statistical Carriers                              
4. Conclusion Collection

Ans: A

2. Classification is a systematic grouping of the units according to their common characteristics. So units having common characteristics are grouped together each of these groups is called.

1. Class
2. Group
3. Logically arranged     
4. Instructions

Ans: A

3. Two cards are drawn without replacement from well stuffed pack of 52 cards. Find the probability that one is a space and other is a queen of red color.

1.      1/50                            

2.      1/51                

3.      1/49

4.      1/52

Ans:B

4. Standard error helps us in:

a. Testing of hypothesis

b. Constructing confidence interval for the statistics

c. Giving reliability measure for the statistic by its reciprocal value

d. All of the above

Ans: D

5. A variable which assumes values 1 and 0 with probabilities p and q = 1-p, is called

a. Binomial distribution

b. Bernoulli distribution

c. Poisson distribution

d. None of the above

Ans: B

6. Height of six students is 163, 173, 168, 156, 162 and 165 cms. Find the arithmetic mean.

a.       164.5 cms       

b.      164     

c.       166     

d.      165.1

Ans: A

7. Two or more events are said to be ________ if the occurrence of one prevents the occurrence of other events.

a. Mutually exclusive events

b. Equi-probable events

c. Independent events

d. Both a and b

Ans: A

8. In a one day cricket match, a bowler bowls 8 over. He gives away 3, 5, 12, 0, 4, 1, 3, 7 runs in these over. Find the mean run rate per over.

a.       43.75

b.      4.375

c.       43.7    

d.      437.5

Ans:B

9. Under this approach the investigator or Researcher assigns probability to the events either from his experience or from past records.

a. Axiomatic Approach

b. Subjective Approach

c. Empirical Approach

d. Statistical Approach

Ans: B

10. Classical probability is also called a

1. Exhaustive
2. Priority
3. Dependent
4. Event

Ans: B

11. Index number represent the relative changes are

1. Expressed in Percentage
2. Relative measure.
3. Expressed in numbers
4. Average

Ans: C

12. Probability plays an important role in;

a. Setting of goals

b. Planning

c. Decision making

d. Budgeting

Ans: C

13. The probability of the two or more independent events occurring together or in succession in the product of their marginal probability.

P (AB) = P (A) x P (B)

1. Joint   
2. Marginal
3. Conditional    
4. Subjective

Ans: C

14. State whether the given statements are true or not:

 Event B and A are statistically independent the conditional probability can be written as

P (B/A) = P (B)

Or

P (A/B) = P/A      

1. True
2. False
3. Cannot say
4. None of the above

Ans: A

15. It is a range of values used to estimate a population parameter:

a. Interval estimate

b. Point estimate

c. Population proportion

d. None of the above

Ans: A

16. An operation that results in a definite outcome is called an:

a. Sample experiment

b. Experiment

c. Random experiment

d. All of the above

Ans; B

17.  The Probability of r successes in n trial is given as:

  n!

r!(n-r)!       P ^r   q ^n-r                        (T/F) 

a. False

b. True

c. Incomplete

d. None of the above

Ans: B

18. Classification is a systematic grouping of the units according to their common characteristics. So units having common characteristics are grouped together, each of these groups is called:

a. Class

b. Group

c. Logically arranged

d. Instructions

Ans: A

19. __________ handles uncertainty systematically and scientifically.

a. Decision-making

b. Probability Theory

c. Ogive analysis

d. Bay’s Probability

Ans: B

20. The following is the frequency distribution of wage of workers of a factory. Find the arithmetic mean.

(a)    129

(b)   128

(c)    120

(d)   121

Ans: A

21. The mean (x) of marks scored by 30 girls of a class is 44%. The mean for 50 boys is 42%. Find the mean for whole class.

a.       40.27%           

b.      41.27%                       

c.       42.75%

d.      42.7%

Ans: C

22. A study of characteristics of units of a population by using statistical device and techniques is called:

a. Statistical investigation

b. Statistical survey

c. Statistical Carriers

d. Conclusion Collection

Ans: A

23. It is defined as the sum of all values divided by number of values:

a. Mean

b. Median

c. Mode

d. Probability

Ans: A

24. Find the geometric mean of 1, 4, 16.

a.       3

b.      4                     

c.       9         

d.      16

Ans: B

25. The frequency distribution is represented by a set of rectangular bars with area proportional to class frequency:

a. Histogram

b. Bar graph

c. Frequency distribution

d. Frequency polygon

Ans: A

26. Find the geometric mean of 1.03, 1.04, 1.06, 1.08.

a.       1.040

b.      1.070

c.       1.40

d.      1.70

Ans: A

27. Graphs used for frequency distribution are:

a. Histogram

b. Frequency polygon

c. Frequency curve

d. All of the above

Ans: D

28. Find the formula of Range:

a.       R = H-L                           

b.      R = H-2L 

c.       R = 2H-L 

d.      R = H-2L

Ans:A

29. If n > _____, then we do not apply z-test unless population S.D. is known.

a.25

b.30

c. 45

d.50

Ans: B

1. Describe different type of probability.

a.       Classical approach

b.      Relative frequency approach

c.       Subjective approach

d.      All of the above

Ans:D

31. State whether it is true or not:

There is no single standard or universal level of significance for testing Hypothesis.

a.       False

b.      True

c.       Cannot say

d.      None of the above

Ans: B

32. Population having a stated or ltd size.

a)      Finite population              

b)      Infinite population           

c)      Judgment 

d)     Parametric

Ans:A

33. The standard deviation of the distribution of sample static is called:

a. Standard size

b. Standard error

c. Standard sample

d. Standard index

Ans: B

34. A sampling method in which a sample is drawn in such a way that it is systematically spread over all the elements of population.

1. Stratified sampling     
2. Systematic sampling
3. Sampling error
4. Sample

Ans: A

35. In this method several varieties of a certain type of commodity under study are used.

a. Explicit Method

b. Implicit Method

c. Computation Method

d. Index method

Ans: A

36. A method of determines correction when the data are not available in numerical form and as a n attractive method of ranking is used.

a.       Rank correction                      

b.      Linear relationship                 

c.       Scatter diagram          

d.      None of the above

Ans: A

37. Movements that occur usually in brief periods of time, without any pattern and are unpredictable in nature.

a. Cyclic Variations

b. Random Variations

c. Seasonal Variations

d. None of the above

Ans: B

38. Analysis of statistical data in concerned with the question of whether there is a relationship between two variables.

a.       Co-efficient of variables  

b.      Correlation analysis          

c.       Inverse analysis    

d.      None of the above

e.       All of the above

Ans: B

39. Ogives is basically:

a. Frequency curve

b. Frequency polygon

c. Cumulative frequency curves

d. None of the above

Ans: C

40. The probability that we associate with an interval estimate is called the

a. Interval estimates

b. Confidence level

c. Random probability

d. Estimation probability

Ans: B

2-marks

41. Define it.

a.       Mode = 3 Median – 2 Mean  

b.      Mode = Median – 3 Mean

c.       Mode = 3 Mean – 2 Mode

d.      None of above

Ans: A

42. Suppose the probability of dialing a wrong number is 0.05. Then, what is the probability of dialing exactly 3 wrong numbers in 100 dials?

a.       0.14

b.      0.15                            

c.       0.4                  

d.      0.16

Ans:A

43. Suppose there are 8 persons from whom we have to select samples of size 3. How many samples can be selected?

a.       56                               

b.      57       

c.       53                   

d.      99

Ans:A

44. A group of 10 students are to be divided into 2 groups of 5 each and seated two tables. How many different ways are there of dividing the 10 students?

a.       200                             

b.      252                 

c.       201                 

d.      250

Ans: A

45. At a dinner party 12 guests had been invited. They are to be divided into 2 groups of 6 each and seated at 2 tables. In how many different who is these guests can be seated?

a.       900

b.      920     

c.       924     

d.      921

Ans:A

46. Data arranged in relation to time. Such data have four components trend, cycle, and seasonal, irregular movements.

a.       Time series

b.      Seasonal index           

c.       Forecasting     

d.      None of the above 

Ans:A

47. An index that links up different fixed base indices to obtain a long comparable series.

a.       Chain index number   

b.      Index number             

c.       Defaulting number     

d.      All of the above

Ans:A

48. An index that measures the change in value between two or more periods of time.

a.       Value index

b.      Weighted index         

c.       Relative method

d.      All of the above

Ans:A

49. Index that compares the change in the price or quantity of a single item between two or more periods of time.

a.       Quantity index                       

b.      Simple index number 

c.       Price index

d.      None of the above

Ans:B

50.  Karl Pearson coefficient of correlation.

a.   r =        Σ x y                b.  r =         x y 

              √ Σx² – y²                           √ Σx² – Σ²                  

c.   r =             x .y                         d.   r =                  x y 

√ (Σx)² – (Σy)²                                     √ Σx²

Ans: A

51. Rank Correlation

a.)  R = 1 _ 6ΣD²                           or                     1 _ 6ΣD²

                N (N²-1)                                                                N3-N

b.)    R = 1 + 6ΣD²

                                    N(N²-1)

c.)     R =  1 _  ΣD²

                     N²-1

d.)    R = 1 _  ΣD²

                   N³-N

Ans: A

52. A method that uses past data to estimate the relationship between two variables.

a.       Regression                        

b.      Regression line     

c.       Slope                    

d.      Standard line

Ans:A

53. A nonparametric test that a concerned with the degrees of agreement between a set of observed ranks (Sample Values) and a theoretical frequency distribution.

a.       Kolmogorav – Smirnev test         

b.      Kurskal – wall is test

c.       Mann – Whitney U test   

d.      None of the above

Ans: A

           

54. Calculate the variance and co-efficient of variation.

a. x= √ Σfd²/N-(Σfd/N)²  xi ,  C.V = s/x                     b. x= √ (Σfd)²/N-Σfd/N xi

 

c. x = √ Σfd/N-Σfd/N xi                                              d. x= √ Σf²/N- Σfd^2/N xi

Ans: A

55. For continuous frequency distribution the median is:

a. M= 1 + [[N/2-m] x c]                                              b. M= L [N/2-m x c]

                            f                                                                              f

c. M= L+ [N/2-M x C]                                                d. None of the above

Ans:A

                          f

56. For the mode the formula as:

a. Z= 1+ [(f-f1) x c]                                                    b. Z= 1+ [f-f1 x c]

            2f-f1 x c                                                                            f1 f1-f2

c. Z= 1+ [(f-f1) x c]                                                    d. Z= 1+ [(f-f1) x c]

2f1–f1-f2                                                                           2f-f1-f2

Ans:A

57. A bag contains 5 white, 7 red and 4 black balls. Four balls are drawn one by one with replacement, what is the probability that none is white?

a.       11/16              

b.      (11/16)⁴                          

c.       16/11              

^d.        [ 11/16]²

Ans:B

58. A class consists of 80 students: 25 of them are girls and 55 boys: 10 of them are rich and the remaining poor; 20 of them are four complexioned. What is the probability of selecting a fair complexioned rich girl?

a.       4/512                                

b.      6/512                    

c.       5/512

d.      2/512

Ans: C

59. Two dice are thrown. Find the probability of getting an odd number on the first dice and a multiple of 3 on the other.

a.       1/2                                    

b.      1/6

c.       1/3            

d.      6/1

Ans:B

60. The odds against A solving a certain problem are 4 to 3 and the odds in favor of B the same problem are 1 to 5. Find the probability that the problem will be solved.

a. 16/21    

b. 16/20                

c. 15/21    

d. 14/21

Ans: A

4-MARKS

61. Match the following:

1. Sampling error                           i. It is also known as inherent error and cannot be avoided. It is not worth to eliminate them completely.

2. Non-sampling error                   ii. They are attributed to factors that can be controlled and eliminated by suitable actions.

3. Biased errors                             iii. It arises in both census and sampling method.

4. Unbiased errors                         iv. The errors that are due to over-estimate and under estimate such that they are equal.

1. 1-I, 2-ii, 3-iii, 4-iv
2. 1-ii, 2-I, 3-iv, 4-iii
3. 1-iii, 2-ii, 3-iv, 4-i
4. 1-iv, 2-iii, 3-ii, 4-i

Ans: A

62. Fishers ‘Ideal’ Method Define which is correct.

a. Po1 = √ Σp1qo/Σpoqo X Σp1q1/Σpoq1 X 100        b. Po1 = √ Σpo/Σqo X Σpo/Σqo X 100

c. Po1 =   √ Σpoq1/Σqo X Σpo/Σqo X 100                  d. Po1 = √ Σpoqo/Σpoqo X Σp1q1/Σpo X 100

Ans: A

63. Collection of primary data cannot be done by anyone of the following methods:

1. Indirect oral interview

2. Information through agencies

3. Direct personal observation

4. Investigation is confidential

5. Accuracy of data is important

e.       1, 2, 3

f.       1, 3, 4

g.      2, 5

h.      4, 5

Ans: D

64. Match the following:

1. Mutually exclusive                          i. there should not be overlapping

2. Suitability                                        ii. Similar units are placed in the same class

3. Homogeneity                                  iii. It should be suitable to objectives of survey

4. Revealing                                        iv. Should bring out essential features of the collected data             

5. Unambiguous                                  v. It should not lead to any confusion.

1. 1-v, 2-iii, 3-iv, 4-I, 5-ii
2. 1-I, 2-iii, 3-ii, 4-iv, 5-v
3. 1-I, 2-ii, 3-iii, 4-iv, 5-v
4. None of the above

Ans: C

65. Find the probability that X=3 for a Binomial Distribution whose mean is 3 and variance is

a. 1672/1792

b. 1795/1800

c. 1792/6591

d. 6561/1792

Ans: C

66. Find P(x=2), given mean and S.D. of the binomial distribution are 4 and √3.

a. 16^c2 (0.73)¹⁴ (0.25)²

b. 16^c3 (0.75)¹⁴ (0.25)²

c. 16^c2 (0.25)² (0.75)¹⁴

d. 16^c2 (0.75)¹⁴(0.25)²

Ans: D

67. State whether the following statements are true:

a. Mean of binomial distribution in npq.

b. Quartile Deviation of normal distribution is 4/5 σ.

c. Mean, median and mode coincide in a normal distribution.

d. “Y” is a Poisson variate if P>0.1 and n>10.

e. “n” and “p” are the parameters of Binomial Distribution.

1. a, b, e
2. c, e
3. c, d, e
4. a, b, c, d, e

Ans: B

68. Suppose 2 house in thousand catches fire in a year and there are 2000 houses in a village, what is the probability. Then

i) None ii) at least one iii) not more than 2 house catches fire

a)i. 0.01832

ii. 0.98168

iii. 0.2366

b)      i. 0.01832

ii. 0.96168

iii. 0.2388

c)      i. 0.01832

ii. 0.98168

iii. 0.2566

d)     i. 0.01832

ii. 0.98166

iii. 0.2366

Ans: A

69. State following are not true:

a.       Populations from which the samples are not selected are not normally distributed.

b.      The effect of various components are not additive.

c.       Analysis variance is useful to test several means.

d.      Another tool applied to test several means in z/t test.

1. a, b, c, d
2. e only
3. a, c, d
4. a, b, d

Ans: D

70. Find Karl Pearson’s Correlation Coefficient given:

X	20	16	12	8	4
Y	22	14	4	12	8

1. 0.79
2. 0.76
3. 0.80
4. 0.70

Ans: D

71. Calculate the Spearman’s Rank Correlation Coefficient between the series A and B given below:

A	57	59	62	63	64	65	55	58	57
B	113	117	126	126	130	129	111	116	112

1. 0.976
2. 0.967
3. 0.797
4. 0.697

Ans:B

72. In Regression Coefficient which statements are true:

a. It has unit attached to it.

b. There is no such nonsense regression.

c. It is not meant for estimation

d. r_xy = r_yx

1. only a
2. c, d only
3. a, b, c only
4. a, b only

Ans: D

73. State whether the given statements are True or not:

1. Tabulation is a systematic arrangement of classified data in row and columns of a table.
2. A frequency distribution in which class intervals are considered is a continuous frequency distribution.
3. Each class interval is specified by two limits which are called class limits.
4. A cumulative frequency curve is called ogive.

1. 1-F, 2-T, 3-F, 4-T
2. 1-T, 2-T, 3-T, 4-T
3. 1-F, 2-F, 3-T, 4-T
4. 1-F, 2-F, 3-T, 4-F

Ans: B

74. Write the following steps in correct sequence:

2. State the level of significance. This gives you the tabulated normal/t – values.
3. Calculate the required values for the test.
4. Conduct the test.
5. State Null Hypothesis (H₀) and alternate hypothesis (H₁).
6. Select the appropriate test from the list.
7. Draw conclusion.

1. 2, 3, 1, 5, 4, 6
2. 1, 2, 3, 5, 4, 6
3. 4, 1, 5, 2, 3, 6
4. All of the above

Ans: C

75. Three dice are thrown simultaneously. Find the probability that:

(i) All of them show the same face

      a.         1          b.         1          c.         1          d.         1

                  36                    6                      5                      4

Ans: A      

(ii) All show distinct bases.

      a          5          b          4          c          5          d          9

                  9                      9                      5                      9

Ans: A

(iii) Two of them show the same face.

                        a          5          b          6          c          5          d          10       

12                      10                    12                    13

                 Ans: A