**STATISTICS**

**STATISTICS MCQs**

1. The names of Francis Galton and Karl Pearson are associated with

1) Probability

2) Correlation

3) Measures of Dispersion

4) Harmonic Mean

Answer: 2

2. The word Regression was used for the first time by

1) Sir Francis Galtom in 1877

2) Sir Francis Galton in 1787

3) Fredrick C. Mills in 1877

4) A.L. Bowley 1877

Answer: 1

3. If Mode and Median of a series are 22 and 21.4 respectively, what will be the value of Arithmetic Mean?

1) 15.99

2) 34.30

3) 21.10

4) 19.33

Answer: 3

4. Statistical averages are of how many types?

1) 2

2) 3

3) 4

4) 5

Answer: 2

5. Karl Pearson coefficient of Correlation is calculated on the basis of measure of

1) Arithmetic mean

2) Standard deviation

3) Arithmetic mean and standard deviation

4) Median and standard deviation

Answer: 3

6. The coefficient of variation of a series is 30% and standard deviation is 15, then its arithmetic mean is

1) 0.5

2) 5.0

3) 2.0

4) 50.00

Answer: 4

7. Statistics diagrams are the instruments of

1) Analysis

2) Interpretation

3) Presentation

4) Collection of data

Answer: 3

8. Method of analysis of variance was proposed by_

1) Sir Ronald A. Fisher(1923)

2) Sir Francis Galton(1877)

3) Wallis and Roberts(1911)

4) Karl Pearson(1932)

Answer: 1

9. Which one of the following is the correct sequence of steps of research ?

1) Problem identification, data analysis, hypothesis, conclusion

2) Hypothesis, data collection, sampling, conclusion, data analysis

3) Thinking about solution, selection of tools, hypothesis, data collection, data analysis

4) Problem identification, hypothesis, data collection, data analysis, conclusion

Ans: 4

10. In the identification of problem the researcher should decide

1) The title and the variables

2) The objectives

3) The variables, title and objectives

4) The title

Ans: 3

11. Probability is known as

1) Deliberate sampling

2) Systematic sampling

3) Stratified sampling

4) Simple random sampling

Ans: 4

12. Which aspect is not related with significance of research ?

1) Research inculcates scientific thinking.

2) Solutions suggested in research are universal

3) Research promotes the habit of logical thinking

4) Spatial and temporal aspects are basis of geographical research

Ans: 2

13. Which of the following is not a quality of good research ?

1) Systematic

2) Methods of data analysis should be appropriate

3) Based on preconceived ideas.

4) Logical

Ans: 3

14. Which is not a method of hypothesis testing ?

1) Chisquire Test

2) Circular Test

3) Student's T. Test

4) Parametric Test

Ans: 2

15. Which type of sampling is done if a population from which a sample drawn does not constitute a homogenous group ?

1) Systematic

2) Random

3) Stratified

4) Area

Ans: 3

16. Which is not a type of the measurement of scale ?

1) Simple Scale

2) Nominal Scale

3) Ordinal Scale

4) Ratio Scale

Ans: 1

17. In report writting, select the correct sequence of the following heads using codes given below : (A) Objectives

(B) Cartographic representation (C) Conclusions (D) Data Collection

1) A, B, C and D

2) A, D, B and C

3) D, A, B and C

4) A, B, D and C

Ans: 2

18. Which is not a characteristic of a research problem ?

1) Relationship between variables

2) Research problem should be in question form

3) Protection of moral judgements

4) Test ability

Ans: 3

19. Which of the following is the correct sequence of increased emphasis on practical action related to research ?

1) Applied - Pure -Policy -Action

2) Pure - Applied- Policy- Action

3) Action -Applied- Policy- Pure

4) Policy - Pure - Applied - Action

Ans: 2

20. The sqaure of standard deviation is called :

1) Variance

2) Precision

3) Regression

4) Relative Standard Deviation

Ans: 1

21. Which of the following is not considered as determinate error ?

1) Operational Error

2) Additive Error

3) Proportional Error

4) Random Error

Ans: 4

22) Which of the following is used to denote a continuous variables?

A) Simple bar

B) Histogram

C) Pie diagram

D) Multiple bar

Ans: 2

23) Likert scale is:

A) Ordinal scale

B) Nominal scale

C) Variance scale

D) Categorical scale

Ans: 1

24) Measuring variation between two different units is done through :

A) Variance

B) Coefficient of variance

C) Standard deviation

D) Range

Ans: 2

25) Z score criteria applicable to :

A) Normal distribution

B) Skewed deviation

C) Chi square test

D) Paired t test

Ans: 1

26) For a Negative skewed data mean will be;

A) Less than median

B) More than median

C) Equal to median

D) One

Ans: 1

27) Q-test is used for detecting:

A) Outliers

B) Interquartile range

C) Difference of means

D) Difference of proportions

Ans: 1

28) About standard Normal curve all is true except:

A) Area = 1

B) S.D = 1

C) Bell shaped

D) Mean and Median = 1

Ans: 4

29) For calculation of sample size for a prevalence study all of the following are necessary except:

A) Prevalence of disease in population

B) Power of the study

C) Significance level

D) Desired precision

Ans: 4

30) True about cluster sampling are all except :

A) Sample size same as simple random

B) It is two stage sampling

C) Cheaper than other methods

D) It is a method for rapid assessment

Ans: 1

31) In a study, variation in cholesterol was seen before and after giving a drug. The test which would give its significance is :

A) Unpaired t test

B) Fischer test

C) Paired t test

D) Chi square test

Ans: 3

32) Appropriate statistical method to compare two proportion is :

A) Chi square test

B) Student’s t test

C) Odds ratio

D) Correlation Coefficient

Ans: 1

33) For testing the statistical significance of the difference in heights of school children:

A) Student’s test

B) Chi square test

C) Paired t test

D) One way analysis of variance (One way ANOV)

Ans: 4

34) Pearson or Spearman coefficient is used for evaluation of :

A) Differences in proportion

B) Comparison of more than 2 means

C) Comparison of variance

D) Correlation

Ans: 4

35) Receiver Operator Characterstic (RO) curve is usually drawn between:

A) Sensitivity & Specificity

B) (1-Sensitivity) & Specificity

C) Sensitivity & (1-Specificity)

D) (1-Sensitivity) & (1-Specificity)

Ans: 3

1) Probability

2) Correlation

3) Measures of Dispersion

4) Harmonic Mean

Answer: 2

2. The word Regression was used for the first time by

1) Sir Francis Galtom in 1877

2) Sir Francis Galton in 1787

3) Fredrick C. Mills in 1877

4) A.L. Bowley 1877

Answer: 1

3. If Mode and Median of a series are 22 and 21.4 respectively, what will be the value of Arithmetic Mean?

1) 15.99

2) 34.30

3) 21.10

4) 19.33

Answer: 3

4. Statistical averages are of how many types?

1) 2

2) 3

3) 4

4) 5

Answer: 2

5. Karl Pearson coefficient of Correlation is calculated on the basis of measure of

1) Arithmetic mean

2) Standard deviation

3) Arithmetic mean and standard deviation

4) Median and standard deviation

Answer: 3

6. The coefficient of variation of a series is 30% and standard deviation is 15, then its arithmetic mean is

1) 0.5

2) 5.0

3) 2.0

4) 50.00

Answer: 4

7. Statistics diagrams are the instruments of

1) Analysis

2) Interpretation

3) Presentation

4) Collection of data

Answer: 3

8. Method of analysis of variance was proposed by_

1) Sir Ronald A. Fisher(1923)

2) Sir Francis Galton(1877)

3) Wallis and Roberts(1911)

4) Karl Pearson(1932)

Answer: 1

9. Which one of the following is the correct sequence of steps of research ?

1) Problem identification, data analysis, hypothesis, conclusion

2) Hypothesis, data collection, sampling, conclusion, data analysis

3) Thinking about solution, selection of tools, hypothesis, data collection, data analysis

4) Problem identification, hypothesis, data collection, data analysis, conclusion

Ans: 4

10. In the identification of problem the researcher should decide

1) The title and the variables

2) The objectives

3) The variables, title and objectives

4) The title

Ans: 3

11. Probability is known as

1) Deliberate sampling

2) Systematic sampling

3) Stratified sampling

4) Simple random sampling

Ans: 4

12. Which aspect is not related with significance of research ?

1) Research inculcates scientific thinking.

2) Solutions suggested in research are universal

3) Research promotes the habit of logical thinking

4) Spatial and temporal aspects are basis of geographical research

Ans: 2

13. Which of the following is not a quality of good research ?

1) Systematic

2) Methods of data analysis should be appropriate

3) Based on preconceived ideas.

4) Logical

Ans: 3

14. Which is not a method of hypothesis testing ?

1) Chisquire Test

2) Circular Test

3) Student's T. Test

4) Parametric Test

Ans: 2

15. Which type of sampling is done if a population from which a sample drawn does not constitute a homogenous group ?

1) Systematic

2) Random

3) Stratified

4) Area

Ans: 3

16. Which is not a type of the measurement of scale ?

1) Simple Scale

2) Nominal Scale

3) Ordinal Scale

4) Ratio Scale

Ans: 1

17. In report writting, select the correct sequence of the following heads using codes given below : (A) Objectives

(B) Cartographic representation (C) Conclusions (D) Data Collection

1) A, B, C and D

2) A, D, B and C

3) D, A, B and C

4) A, B, D and C

Ans: 2

18. Which is not a characteristic of a research problem ?

1) Relationship between variables

2) Research problem should be in question form

3) Protection of moral judgements

4) Test ability

Ans: 3

19. Which of the following is the correct sequence of increased emphasis on practical action related to research ?

1) Applied - Pure -Policy -Action

2) Pure - Applied- Policy- Action

3) Action -Applied- Policy- Pure

4) Policy - Pure - Applied - Action

Ans: 2

20. The sqaure of standard deviation is called :

1) Variance

2) Precision

3) Regression

4) Relative Standard Deviation

Ans: 1

21. Which of the following is not considered as determinate error ?

1) Operational Error

2) Additive Error

3) Proportional Error

4) Random Error

Ans: 4

22) Which of the following is used to denote a continuous variables?

A) Simple bar

B) Histogram

C) Pie diagram

D) Multiple bar

Ans: 2

23) Likert scale is:

A) Ordinal scale

B) Nominal scale

C) Variance scale

D) Categorical scale

Ans: 1

24) Measuring variation between two different units is done through :

A) Variance

B) Coefficient of variance

C) Standard deviation

D) Range

Ans: 2

25) Z score criteria applicable to :

A) Normal distribution

B) Skewed deviation

C) Chi square test

D) Paired t test

Ans: 1

26) For a Negative skewed data mean will be;

A) Less than median

B) More than median

C) Equal to median

D) One

Ans: 1

27) Q-test is used for detecting:

A) Outliers

B) Interquartile range

C) Difference of means

D) Difference of proportions

Ans: 1

28) About standard Normal curve all is true except:

A) Area = 1

B) S.D = 1

C) Bell shaped

D) Mean and Median = 1

Ans: 4

29) For calculation of sample size for a prevalence study all of the following are necessary except:

A) Prevalence of disease in population

B) Power of the study

C) Significance level

D) Desired precision

Ans: 4

30) True about cluster sampling are all except :

A) Sample size same as simple random

B) It is two stage sampling

C) Cheaper than other methods

D) It is a method for rapid assessment

Ans: 1

31) In a study, variation in cholesterol was seen before and after giving a drug. The test which would give its significance is :

A) Unpaired t test

B) Fischer test

C) Paired t test

D) Chi square test

Ans: 3

32) Appropriate statistical method to compare two proportion is :

A) Chi square test

B) Student’s t test

C) Odds ratio

D) Correlation Coefficient

Ans: 1

33) For testing the statistical significance of the difference in heights of school children:

A) Student’s test

B) Chi square test

C) Paired t test

D) One way analysis of variance (One way ANOV)

Ans: 4

34) Pearson or Spearman coefficient is used for evaluation of :

A) Differences in proportion

B) Comparison of more than 2 means

C) Comparison of variance

D) Correlation

Ans: 4

35) Receiver Operator Characterstic (RO) curve is usually drawn between:

A) Sensitivity & Specificity

B) (1-Sensitivity) & Specificity

C) Sensitivity & (1-Specificity)

D) (1-Sensitivity) & (1-Specificity)

Ans: 3

36. “The systematic and controlled handling of variables to see if treatments will create expected result” is an essential step in

A:-Ex Post facto Research

B:-Scientific Method

C:-Diagnostic method

D:-Exploratory research

Correct Answer:- Option-B

37. In a sponsored research which of the following action of the sponsor is in compliance with ethical considerations

A:- Instructions on How to do research

B:- Instructions on what is to be reported and not

C:-Instructions on purposes of research

D:- Instructions on not to conceal the sponsor

Correct Answer:- Option-D

38. Reliability in research stands for

A:-Replicability

B:-Validity

C:-Measureability

D:-Comparability

Correct Answer:- Option-A

39. Insufficient evidence in research leads to

A:-Faulty analysis

B:-Over generalization

C:-Poor sampling

D:- Wrong methodology

Correct Answer:- Option-B

40. Citation index is directly related to

A:-Periodicity of a journal

B:-Popularity of a journal

C:-Impact factor of a journal

D:- Publication of a journal

Correct Answer:- Option-C

41. For two random variables X and Y, the relation E(XY)=E(X)E(Y) holds good

A:-if X and Y are statistically independent.

B:-for all X and Y.

C:-if X and Y are identical.

D:-none of these.

Correct Answer:- Option-A

A:-Ex Post facto Research

B:-Scientific Method

C:-Diagnostic method

D:-Exploratory research

Correct Answer:- Option-B

37. In a sponsored research which of the following action of the sponsor is in compliance with ethical considerations

A:- Instructions on How to do research

B:- Instructions on what is to be reported and not

C:-Instructions on purposes of research

D:- Instructions on not to conceal the sponsor

Correct Answer:- Option-D

38. Reliability in research stands for

A:-Replicability

B:-Validity

C:-Measureability

D:-Comparability

Correct Answer:- Option-A

39. Insufficient evidence in research leads to

A:-Faulty analysis

B:-Over generalization

C:-Poor sampling

D:- Wrong methodology

Correct Answer:- Option-B

40. Citation index is directly related to

A:-Periodicity of a journal

B:-Popularity of a journal

C:-Impact factor of a journal

D:- Publication of a journal

Correct Answer:- Option-C

41. For two random variables X and Y, the relation E(XY)=E(X)E(Y) holds good

A:-if X and Y are statistically independent.

B:-for all X and Y.

C:-if X and Y are identical.

D:-none of these.

Correct Answer:- Option-A

42. In the simultaneous tossing of two perfect coins, the probability of having atleast one head is

A:-12

B:-14

C:-34

D:-1

Correct Answer:- Option-C

43. If P1 (x) and P2 (x) be the marginal probability functions of two independent discrete random variables X and Y, then their joint probability function P(x,y)=

A:-P1(x)/P2(y)

B:-P1(x)P2(y)

C:-P2(y)/P1(x)

D:-None of these

Correct Answer:- Option-B

44. Var(2X± 3) if Var(X)=1 is

A:-5

B:-13

C:-4

D:-none of these.

Correct Answer:- Option-C

45. The height of persons in a country is a random variable of the type

A:-continuous random variable

B:-discrete random variable

C:-neither discrete nor continuous random variable

D:-continuou as well as discrete random variable

Correct Answer:- Option-A

46. A probability distribution in which mean is equal to variance is

A:-Binomial

B:-Gamma

C:-Normal

D:-Poisson

Correct Answer:- Option-D

47. The skewness in a binomial distribution will be zero, if

A:-p<1/2

B:-p>1/2

C:-p<q

D:-p=1/2

Correct Answer:- Option-D

48. The coefficient of variation of Poisson distribution with mean 4 is

A:-1/4

B:-2/4

C:-4

D:-2

Correct Answer:- Option-B

49. If X is a normal variate representing the income in Rs. per day with mean=50 and S.D=10. If the number of workers in a factory is 1200, then the number of workers having income more than Rs. 62.00 per =0.3849 where Z is a standard normal variate)

A:-462

B:-738

C:-138

D:-none of the above.

Correct Answer:- Option-C

50. The distribution for which mode does not exist is

A:-normal

B:-t-distribution

C:-continuous rectangular distribution

D:-F distribution

Correct Answer:- Option-C

A:-12

B:-14

C:-34

D:-1

Correct Answer:- Option-C

43. If P1 (x) and P2 (x) be the marginal probability functions of two independent discrete random variables X and Y, then their joint probability function P(x,y)=

A:-P1(x)/P2(y)

B:-P1(x)P2(y)

C:-P2(y)/P1(x)

D:-None of these

Correct Answer:- Option-B

44. Var(2X± 3) if Var(X)=1 is

A:-5

B:-13

C:-4

D:-none of these.

Correct Answer:- Option-C

45. The height of persons in a country is a random variable of the type

A:-continuous random variable

B:-discrete random variable

C:-neither discrete nor continuous random variable

D:-continuou as well as discrete random variable

Correct Answer:- Option-A

46. A probability distribution in which mean is equal to variance is

A:-Binomial

B:-Gamma

C:-Normal

D:-Poisson

Correct Answer:- Option-D

47. The skewness in a binomial distribution will be zero, if

A:-p<1/2

B:-p>1/2

C:-p<q

D:-p=1/2

Correct Answer:- Option-D

48. The coefficient of variation of Poisson distribution with mean 4 is

A:-1/4

B:-2/4

C:-4

D:-2

Correct Answer:- Option-B

49. If X is a normal variate representing the income in Rs. per day with mean=50 and S.D=10. If the number of workers in a factory is 1200, then the number of workers having income more than Rs. 62.00 per =0.3849 where Z is a standard normal variate)

A:-462

B:-738

C:-138

D:-none of the above.

Correct Answer:- Option-C

50. The distribution for which mode does not exist is

A:-normal

B:-t-distribution

C:-continuous rectangular distribution

D:-F distribution

Correct Answer:- Option-C

51. A box contains 12 items out of which 4 are defective. A person selects 6 items from the box. The expected number of defective items out of his selected items is

A:-2

B:-3

C:-3/2

D:-none of the above.

Correct Answer:- Option-A

52. If Z is a standard normal variate, the proportion of items lying between z=-0.5 and z=-3.0 is

A:-0.4987

B:-0.1915

C:-0.3072

D:-0.3098

Correct Answer:- Option-C

53. Factorization theorem for sufficiency is known as

A:-Rao-Blackwell theorem

B:-Cramer-Rao theorem

C:-Chapman-Robins theorem

D:-Fisher-Neyman theorem

Correct Answer:- Option-D

54. If the expected value of an estimator is not equal to its parametric function τ(Θ) , it is said to be a

A:-unbiased estimator

B:-biased estimator

C:-consistent estimator

D:-none of the above.

Correct Answer:- Option-B

55. The sample median is _______________ estimate for the mean of normal population.

A:-unbiased

B:-consistent

C:-unbiased and consistent

D:-none of the above.

Correct Answer:- Option-C

56. If a sufficient estimator exists it is a function of the _______ estimator.

A:-moment estimator

B:-minimum chisquare estimator

C:-maximum likelihood estimator

D:-none of the above

Correct Answer:- Option-C

57. The credit of inventing the method of moments for estimating the parameter goes to

A:-R. A. Fisher

B:-J. Neyman

C:-Laplace

D:-Karl Pearson

Correct Answer:- Option-D

58. Cramer-Rao inequality with regard to the variance of an estimator provides

A:-upper bound on the variance

B:-lower bound on the variance

C:-asymptotic variance of an estimator

D:-none of the above

Correct Answer:- Option-B

59. Estimate and Estimator are

A:-synonyms

B:-related to population

C:-different

D:-none of the above

Correct Answer:- Option-C

60. The idea of testing of hypothesis was first set forth by

A:-R.A.Fisher

B:-J.Neyman

C:-E.L.Lehman

D:-A.Wald

Correct Answer:- Option-B

61. A wrong decision about H0 leads to

A:-one kind of error

B:-two kinds of errors

C:-three kinds of errors

D:-four kinds of errors

Correct Answer:- Option-B

62. In terms of type II error β and θ , the true parameter, the function 1-β(θ) is called

A:-power of the test

B:-power function

C:-OC function

D:-none of the above

Correct Answer:- Option-B

63. Testing H0:µ =1500 against µ<1500 leads to

A:-one-sided lower tailed test

B:-one-sided upper tailed test

C:-two-tailed test

D:-all the above

Correct Answer:- Option-A

64. The mean difference between 9 paired observations is 15.0 and the standard deviation of differences is 5.0. The value of statistic t is

A:-27

B:-9

C:-3

D:-zero

Correct Answer:- Option-B

65. Range of statistic t is

A:--1 to 1

B:-−∞ to ∞

C:-0 to ∞

D:-0 to 1

Correct Answer:- Option-B

66. Given the following eight sample values -4, -3, -3, 0, 3, 3, 4, 4 the value of student's t-statistc to test H0 : µ =0 is

A:-2.73

B:-0.97

C:-3.30

D:-0.41

Correct Answer:- Option-D

67. In a contingency table, the expected frequencies are computed under

A:-null hypothesis H0

B:-alternative hypothesis H1

C:-H0 and H1 both

D:-no consideration of hypothesis

Correct Answer:- Option-A

68. The term regression was introduced by

A:-R.A.Fisher

B:-Sir Francis Galton

C:-Karl Pearson

D:-none of the above

Correct Answer:- Option-B

69. If βYX and βXY are two regression coefficients they have

A:-same sign

B:-opposite sign

C:-either same or opposite signs

D:-nothing can be said

Correct Answer:- Option-A

70. If a constant 50 is subtracted from each of the value of X and Y, the regression coefficient is

A:-reduced by 50

B:-150 th of the original regression coefficient

C:-increased by 50

D:-not changed

Correct Answer:- Option-D

71. If ρ is the simple correlation coefficient, the quantity ρ2 is known as

A:-coefficient of determination

B:-coefficient of non-determination

C:-coefficient of alienation

D:-none of the above

Correct Answer:- Option-A

72. The range of simple correlation coefficient is

A:-0 to ∞

B:--∞ to ∞

C:-0 to 1

D:--1 to 1

Correct Answer:- Option-D

73. The hypothesis for a specific known value of ρ can be tested by

A:-t-test

B:-Z-test

C:-χ2 -test

D:-F-test

Correct Answer:- Option-B

74. A measure of linear association of a variable with a number of other variables is known as

A:-partial correlation

B:-simple correlation

C:-autocorrelation

D:-multiple correlation

Correct Answer:- Option-D

75. Given the regression lines X+2Y-5=0, 2X+3Y-8=0 and Var(X)=12, the value of Var(Y) is

A:-16

B:-34

C:-43

D:-4

Correct Answer:- Option-D

76. The sales of a departmental store on Dushera and Diwali are associated with the component of a time series

A:-secular trend

B:-irregular variation

C:-seasonal variation

D:-all the above

Correct Answer:- Option-C

77. Which index satisfies factor reversal test?

A:-Paasche's index

B:-Laspeyer's index

C:-Walsch price index

D:-Fisher's ideal index

Correct Answer:- Option-D

78. Control chart consists of

A:-three control lines

B:-upper and lower control lines

C:-the level of the process

D:-all the above

Correct Answer:- Option-A

79. Replication in an experiment means

A:-the number of blocks

B:-the number of times a treatment occurs in an experiment

C:-total number of treatments

D:-none of the above

Correct Answer:- Option-B

80. Local control in experimental designs is meant to

A:-increase the efficiency of the design

B:-reduce experimental error

C:-to form homogeneous blocks

D:-all the above

Correct Answer:- Option-D

81. Moving average method of fitting trend in a time series data removes the effect of

A:-long term movements

B:-seasonal variation

C:-cyclic variations

D:-short-term movements

Correct Answer:- Option-D

A:-2

B:-3

C:-3/2

D:-none of the above.

Correct Answer:- Option-A

52. If Z is a standard normal variate, the proportion of items lying between z=-0.5 and z=-3.0 is

A:-0.4987

B:-0.1915

C:-0.3072

D:-0.3098

Correct Answer:- Option-C

53. Factorization theorem for sufficiency is known as

A:-Rao-Blackwell theorem

B:-Cramer-Rao theorem

C:-Chapman-Robins theorem

D:-Fisher-Neyman theorem

Correct Answer:- Option-D

54. If the expected value of an estimator is not equal to its parametric function τ(Θ) , it is said to be a

A:-unbiased estimator

B:-biased estimator

C:-consistent estimator

D:-none of the above.

Correct Answer:- Option-B

55. The sample median is _______________ estimate for the mean of normal population.

A:-unbiased

B:-consistent

C:-unbiased and consistent

D:-none of the above.

Correct Answer:- Option-C

56. If a sufficient estimator exists it is a function of the _______ estimator.

A:-moment estimator

B:-minimum chisquare estimator

C:-maximum likelihood estimator

D:-none of the above

Correct Answer:- Option-C

57. The credit of inventing the method of moments for estimating the parameter goes to

A:-R. A. Fisher

B:-J. Neyman

C:-Laplace

D:-Karl Pearson

Correct Answer:- Option-D

58. Cramer-Rao inequality with regard to the variance of an estimator provides

A:-upper bound on the variance

B:-lower bound on the variance

C:-asymptotic variance of an estimator

D:-none of the above

Correct Answer:- Option-B

59. Estimate and Estimator are

A:-synonyms

B:-related to population

C:-different

D:-none of the above

Correct Answer:- Option-C

60. The idea of testing of hypothesis was first set forth by

A:-R.A.Fisher

B:-J.Neyman

C:-E.L.Lehman

D:-A.Wald

Correct Answer:- Option-B

61. A wrong decision about H0 leads to

A:-one kind of error

B:-two kinds of errors

C:-three kinds of errors

D:-four kinds of errors

Correct Answer:- Option-B

62. In terms of type II error β and θ , the true parameter, the function 1-β(θ) is called

A:-power of the test

B:-power function

C:-OC function

D:-none of the above

Correct Answer:- Option-B

63. Testing H0:µ =1500 against µ<1500 leads to

A:-one-sided lower tailed test

B:-one-sided upper tailed test

C:-two-tailed test

D:-all the above

Correct Answer:- Option-A

64. The mean difference between 9 paired observations is 15.0 and the standard deviation of differences is 5.0. The value of statistic t is

A:-27

B:-9

C:-3

D:-zero

Correct Answer:- Option-B

65. Range of statistic t is

A:--1 to 1

B:-−∞ to ∞

C:-0 to ∞

D:-0 to 1

Correct Answer:- Option-B

66. Given the following eight sample values -4, -3, -3, 0, 3, 3, 4, 4 the value of student's t-statistc to test H0 : µ =0 is

A:-2.73

B:-0.97

C:-3.30

D:-0.41

Correct Answer:- Option-D

67. In a contingency table, the expected frequencies are computed under

A:-null hypothesis H0

B:-alternative hypothesis H1

C:-H0 and H1 both

D:-no consideration of hypothesis

Correct Answer:- Option-A

68. The term regression was introduced by

A:-R.A.Fisher

B:-Sir Francis Galton

C:-Karl Pearson

D:-none of the above

Correct Answer:- Option-B

69. If βYX and βXY are two regression coefficients they have

A:-same sign

B:-opposite sign

C:-either same or opposite signs

D:-nothing can be said

Correct Answer:- Option-A

70. If a constant 50 is subtracted from each of the value of X and Y, the regression coefficient is

A:-reduced by 50

B:-150 th of the original regression coefficient

C:-increased by 50

D:-not changed

Correct Answer:- Option-D

71. If ρ is the simple correlation coefficient, the quantity ρ2 is known as

A:-coefficient of determination

B:-coefficient of non-determination

C:-coefficient of alienation

D:-none of the above

Correct Answer:- Option-A

72. The range of simple correlation coefficient is

A:-0 to ∞

B:--∞ to ∞

C:-0 to 1

D:--1 to 1

Correct Answer:- Option-D

73. The hypothesis for a specific known value of ρ can be tested by

A:-t-test

B:-Z-test

C:-χ2 -test

D:-F-test

Correct Answer:- Option-B

74. A measure of linear association of a variable with a number of other variables is known as

A:-partial correlation

B:-simple correlation

C:-autocorrelation

D:-multiple correlation

Correct Answer:- Option-D

75. Given the regression lines X+2Y-5=0, 2X+3Y-8=0 and Var(X)=12, the value of Var(Y) is

A:-16

B:-34

C:-43

D:-4

Correct Answer:- Option-D

76. The sales of a departmental store on Dushera and Diwali are associated with the component of a time series

A:-secular trend

B:-irregular variation

C:-seasonal variation

D:-all the above

Correct Answer:- Option-C

77. Which index satisfies factor reversal test?

A:-Paasche's index

B:-Laspeyer's index

C:-Walsch price index

D:-Fisher's ideal index

Correct Answer:- Option-D

78. Control chart consists of

A:-three control lines

B:-upper and lower control lines

C:-the level of the process

D:-all the above

Correct Answer:- Option-A

79. Replication in an experiment means

A:-the number of blocks

B:-the number of times a treatment occurs in an experiment

C:-total number of treatments

D:-none of the above

Correct Answer:- Option-B

80. Local control in experimental designs is meant to

A:-increase the efficiency of the design

B:-reduce experimental error

C:-to form homogeneous blocks

D:-all the above

Correct Answer:- Option-D

81. Moving average method of fitting trend in a time series data removes the effect of

A:-long term movements

B:-seasonal variation

C:-cyclic variations

D:-short-term movements

Correct Answer:- Option-D

82. Which measure of location will be suitable to compare heights of students in two classes?

A:-Mean

B:-Median

C:-Mode

D:-None of these

Correct Answer:- Option-A

83. The geometric mean of 2, 4, 16 and 32 is

A:-6

B:-7

C:-8

D:-9

Correct Answer:- Option-C

84. The strength of seven colleges in a city are 385,1748,1343,1935,786,2874 and 2108. Then the median strength is

A:-1935

B:-1748

C:-1343

D:-2874

Correct Answer:- Option-B

85. The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is actually 110. Therefore, the true mean is ___ and the true median is _____ .

A:-50.1, 52

B:-50.9, 53

C:-51.1, 52

D:-50, 53

Correct Answer:- Option-A

86. 10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of a combined set is given by

A:-15

B:-10

C:-8.5

D:-7.5

Correct Answer:- Option-C

87. A distribution with more than two modes is called

A:-unimodal

B:-bimodal

C:-multimodal

D:-none of these

Correct Answer:- Option-C

88. The algebraic sum of the deviations of a set of n values from their arithmetic mean is

A:-n

B:-0

C:-1

D:-none of these

Correct Answer:- Option-B

89. The mean of 20 observations is 15. On checking it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is

A:-15.15

B:-16.15

C:-17.15

D:-14.15

Correct Answer:- Option-A

90. Sum of absolute deviations about median is

A:-least

B:-greatest

C:-zero

D:-equal

Correct Answer:- Option-A

91. If each of a set of observations of a variable is multiplied by a constant (non-zero) value, the variance of the resultant variable

A:-is unaltered

B:-increases

C:-decreases

D:-is unknown

Correct Answer:- Option-B

92. The standard deviation of a distribution is 5. The value of the fourth central moment µ4 in order that the distribution be mesokurtic should be

A:-equal to 3

B:-greater than 1875

C:-equal to 1875

D:-less than 1875

Correct Answer:- Option-C

93. In a frequency curve of scores the mode was found to be higher than the mean. This shows that the distribution is

A:-symmetric

B:-negatively skewed

C:-positively skewed

D:-normal

Correct Answer:- Option-B

94. A coin is tossed three times in succession, the number of sample points in sample space is

A:-6

B:-8

C:-3

D:-4

Correct Answer:- Option-B

95. If A and B are two independent events, the probability that both A and B occur is 1/8 and the probability that neither of them occurs is 3/8 . The probability of the occurrence of A is

A:-1/2

B:-1/3

C:-1/4

D:-1/5

Correct Answer:- Option-A

96:-In a Time series data, the two main components which cause lack of stationarity are

A:-Seasonal and irregular variations

B:-Cyclic and irregular variations

C:-Trend and cyclic variations

D:-Trend and seasonal variations

Ans: D

97:-In the ARMA (1, 1) model `Z_t = ``phi Z_{t-1} + epsilon _t - theta epsilon_{t-1}` the condition for stationarity

and invertilibility are respectively

A:-` | phi | <= 1 and | theta | < 1` with `phi != theta`

B:-` | phi | <= 1 and | theta | < 1` with `phi = theta`

C:-` | phi | > 1 and | theta | > 1` with `phi!= theta`

D:-` | phi | > 1 and | theta | > 1` with `phi = theta`

Ans: A

98:-In a Linear programming Problem with `n + m` variables and `m` constraints the number of basic solutions is

A:-` ((n+m),(m))`

B:-`((n),(m))`

C:-`((m),(n))`

D:-`((n+m),(n-m))`

Ans: A

99:-If the demand curve is of the form `p = ae^{-bx}` , where `p` is the price and `x` is the demand, then the

price elasticity of demand is

A:-`eta_p = bx`

B:-`eta_p = - bx`

C:-`eta_p = 1//bx`

D:-`eta_p = - 1 // bx`

Ans: C

100:-The Engel's curves for constant prices and those for constant incomes are respectively

A:-Concave and Convex

B:-Convex and Concave

C:-Both Concave

D:-Both Convex

Ans: B

A:-Mean

B:-Median

C:-Mode

D:-None of these

Correct Answer:- Option-A

83. The geometric mean of 2, 4, 16 and 32 is

A:-6

B:-7

C:-8

D:-9

Correct Answer:- Option-C

84. The strength of seven colleges in a city are 385,1748,1343,1935,786,2874 and 2108. Then the median strength is

A:-1935

B:-1748

C:-1343

D:-2874

Correct Answer:- Option-B

85. The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is actually 110. Therefore, the true mean is ___ and the true median is _____ .

A:-50.1, 52

B:-50.9, 53

C:-51.1, 52

D:-50, 53

Correct Answer:- Option-A

86. 10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of a combined set is given by

A:-15

B:-10

C:-8.5

D:-7.5

Correct Answer:- Option-C

87. A distribution with more than two modes is called

A:-unimodal

B:-bimodal

C:-multimodal

D:-none of these

Correct Answer:- Option-C

88. The algebraic sum of the deviations of a set of n values from their arithmetic mean is

A:-n

B:-0

C:-1

D:-none of these

Correct Answer:- Option-B

89. The mean of 20 observations is 15. On checking it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is

A:-15.15

B:-16.15

C:-17.15

D:-14.15

Correct Answer:- Option-A

90. Sum of absolute deviations about median is

A:-least

B:-greatest

C:-zero

D:-equal

Correct Answer:- Option-A

91. If each of a set of observations of a variable is multiplied by a constant (non-zero) value, the variance of the resultant variable

A:-is unaltered

B:-increases

C:-decreases

D:-is unknown

Correct Answer:- Option-B

92. The standard deviation of a distribution is 5. The value of the fourth central moment µ4 in order that the distribution be mesokurtic should be

A:-equal to 3

B:-greater than 1875

C:-equal to 1875

D:-less than 1875

Correct Answer:- Option-C

93. In a frequency curve of scores the mode was found to be higher than the mean. This shows that the distribution is

A:-symmetric

B:-negatively skewed

C:-positively skewed

D:-normal

Correct Answer:- Option-B

94. A coin is tossed three times in succession, the number of sample points in sample space is

A:-6

B:-8

C:-3

D:-4

Correct Answer:- Option-B

95. If A and B are two independent events, the probability that both A and B occur is 1/8 and the probability that neither of them occurs is 3/8 . The probability of the occurrence of A is

A:-1/2

B:-1/3

C:-1/4

D:-1/5

Correct Answer:- Option-A

96:-In a Time series data, the two main components which cause lack of stationarity are

A:-Seasonal and irregular variations

B:-Cyclic and irregular variations

C:-Trend and cyclic variations

D:-Trend and seasonal variations

Ans: D

97:-In the ARMA (1, 1) model `Z_t = ``phi Z_{t-1} + epsilon _t - theta epsilon_{t-1}` the condition for stationarity

and invertilibility are respectively

A:-` | phi | <= 1 and | theta | < 1` with `phi != theta`

B:-` | phi | <= 1 and | theta | < 1` with `phi = theta`

C:-` | phi | > 1 and | theta | > 1` with `phi!= theta`

D:-` | phi | > 1 and | theta | > 1` with `phi = theta`

Ans: A

98:-In a Linear programming Problem with `n + m` variables and `m` constraints the number of basic solutions is

A:-` ((n+m),(m))`

B:-`((n),(m))`

C:-`((m),(n))`

D:-`((n+m),(n-m))`

Ans: A

99:-If the demand curve is of the form `p = ae^{-bx}` , where `p` is the price and `x` is the demand, then the

price elasticity of demand is

A:-`eta_p = bx`

B:-`eta_p = - bx`

C:-`eta_p = 1//bx`

D:-`eta_p = - 1 // bx`

Ans: C

100:-The Engel's curves for constant prices and those for constant incomes are respectively

A:-Concave and Convex

B:-Convex and Concave

C:-Both Concave

D:-Both Convex

Ans: B