**STATISTICS-PAGE 2**

**STATISTICS MCQ- PAGE 2**

1:-If `A_n={(A if n "is odd"),(B if n "is even"):}`

then lim inf `A_n=`` `

A:-`AuuB`

B:-`quadAnnB`

C:-`quadA` Δ`quadB`

D:-`phi`

Ans: B

2:-Which of the following statement(s) is/are wrong?

I : A monotone field in not a sigma field

II : A sigma field is a monotone field

A:-I alone

B:-II alone

C:-Neither I nor II

D:-Both I and II

Ans: A

3:-If `quadmu_1` is a measure defined on a sigma field `quadfrA_1` and `quadmu_2` is a measure defined on a

sigma field `quadfrA_2` , then `quadmu_1+mu_2` is a measure only when

A:-`quadfrA_1subfrA_2`

B:-`quadfrA_1supfrA_2`

C:- `quadfrA_1=frA_2`

D:-`quadfrA_1!=frA_2`

Ans: C

4:-Which of the following statement(s) is/are true?

A : Every subsets of are Borel sets

B : Every Borel set in measurable

A:-A alone

B:-B alone

C:-Neither A nor B

D:-Both A and B

Ans: B

5:-Let `quadI = (0, 1)` , be the Borel field of subsets of `quadI` and `mu` is the Lebesgue measure on

. For `quadn = 1, 2,....,` if `quadA_n=(0,1/n), mu(lim "sup" A_n)=`

A:-0

B:-0.5

C:-1

D:-`1/n`

Ans: A

6:-Let `quadW` be the subspace of generated by the vectors (1, -2, 5, -3), (2, 3, 1, -4) and (3, 8, -3, -5). Then

the dimension of `quadW` is

A:-4

B:-3

C:-2

D:-1

Ans: C

7:-For any arbitrary matrices `quadA` and `quadB` , the sum of ranks of `quadA` and `quadB` is always

A:-less than rank `quad(A+B)`

B:-less than or equal to rank`quad(A+B)`

C:-greater than rank`quad(A+B)`

D:-greater than or equal to rank`quad(A+B)`

Ans: D

8:-Let `quadA` and `quadB` are `quadnxxn` square matrices. Then the eigen values of `quadAB` are same as

the eigen values of

A:-`quadA+B`

B:-`quadA-B`

C:-`quadB-A`

D:-`quadBA`

Ans: D

9:-The quadratic polynomial corresponds to the matrix `quadA=((1,0,1/2),(0,0,-1),(1/2,-1,0))` ` ` is

A:-`quadx^2+1/2xz-xy`

B:-`quadx^2-2yz+xz`

C:-`quadx^2+1/2yz-xy`

D:-`quadx^2+yz-2xz`

Ans: B

10:-Let `quadP` be an `quadmxxm` orthogonal matrix, `quadQ` be an `quadnxxn` orthogonal matrix and `quadA`

any `quadmxxn` matrix. If `quadA^T` denote the transpose of `quadA` and `quadA^-` denote the generalized inverse of

`A` , then the generalized inverse of `quadPAQ` is

A:-`quadP^TA^{-}Q^T`

B:-`quadQ^TA^{-}P^T`

C:-`quadPA^{-}Q`

D:-`quadQA^{-}P`

Ans: B

11:-If `quad{A_n}` is a sequence of events on a probability space (Ω,`quadA,P)` such that `quadA_n->A`

as `quadn->oo` , then what is the value of lim`quadP(A_n)` ?

A:-zero

B:-one

C:-`quadP(A)`

D:-need not exist

Ans: C

12:-If `quadA` and `quadB` are mutually exclusive events, each with positive probabilities, then they are

A:-independent events

B:-dependent events

C:-equally likely events

D:-exhaustive events

Ans: B

13:-If `quad{A_n}` is a sequence of events such that `quadsum_(k=1)^ooP(A_k)=oo` , then

`quadP(lim"sup"A_n)=1` provided events are

A:-equally likely

B:-Mutually exclusive

C:-independent

D:-pair-wise mutually exclusive

Ans: C

14:-Let `quad{A_n}` be a sequence of events such that `quadB_1=A_1` and `quadB_k=A^c_1

A^c_2...` `A_{k-1}^c A_k` for `quadk>=2` , in which `quadA^c` is the complement of `quadA` . Then the sequence of

events `quad{B_n}` are

A:-Pair-wise independent

B:-Mutually independent

C:-Mutually dependent

D:-Pair-wise mutually exclusive

Ans: D

15:-If `quadX` is a random variable with finite expectation, then the value of `quadxP(X<-x)` as `quadx->oo` is

A:-infinity

B:-unity

C:-zero

D:-indeterminate

Ans: C

16:-If `quadX` is a symmetric random variable with distribution function `quadF` and real valued characteristic

function Φ, then for any `quadx` in ,`quadF(x)=`

A:-`quadF(-x)`

B:-`quadF(-x-0)`

C:-`quadF(-x-0)-1`

D:-`quad1-F(-x-0)`

Ans: D

17:-If the characteristic function Φ of distribution function `quadF` is absolutely integrable on , then for

any`quadx` in , `quad f'={dF(x)}/dx` is

A:-bounded

B:-uniformly continuous

C:-both (1) and (2)

D:-Neither (1) nor (2)

Ans: C

18:-Let `quadX` and `quadX_n` be independent standard normal variables on a probability space (Ω,`quadfrA,P)` `

`, for `quadn>=1` . Then which of the following is not true?

A:-`X_nstackrel(P)(->)X`

B:-`X_nstackrel(d)(->)X`

C:-`quadE(X_n-X)=0`

D:-`quadVar(X_n-X)=2`

Ans: A

19:-The sequence `quad{X_n}` of independent random variables, each with finite second moment, obeys SLLN if

A:-`quadsum_(k=1)^ooVar(X_k)<oo`

B:-`quadsum_(k=1)^oo{Var(X_k)}/k<oo`

C:-`quadsum_(k=1)^oo{Var(X_k)}/sqrt(k)<oo`

D:-`quadsum_(k=1)^oo{Var(X_k)}/k^2<oo`

Ans: D

20:-Let `quad{X_n}` sequence of independent random variables with

`quadP(X_k=+-k)=1/2k^-Lambda` and `quadP(X_k=0)=1-k^-Lambda` , for `quadk>=1`

Then the sequence does not obey CLT if

A:-`quadLambda=0`

B:-`quadLambda=1`

C:-`quadLambdain(0,1/2)`

D:-`quadLambdain(1/2,1)`

Ans: B

then lim inf `A_n=`` `

A:-`AuuB`

B:-`quadAnnB`

C:-`quadA` Δ`quadB`

D:-`phi`

Ans: B

2:-Which of the following statement(s) is/are wrong?

I : A monotone field in not a sigma field

II : A sigma field is a monotone field

A:-I alone

B:-II alone

C:-Neither I nor II

D:-Both I and II

Ans: A

3:-If `quadmu_1` is a measure defined on a sigma field `quadfrA_1` and `quadmu_2` is a measure defined on a

sigma field `quadfrA_2` , then `quadmu_1+mu_2` is a measure only when

A:-`quadfrA_1subfrA_2`

B:-`quadfrA_1supfrA_2`

C:- `quadfrA_1=frA_2`

D:-`quadfrA_1!=frA_2`

Ans: C

4:-Which of the following statement(s) is/are true?

A : Every subsets of are Borel sets

B : Every Borel set in measurable

A:-A alone

B:-B alone

C:-Neither A nor B

D:-Both A and B

Ans: B

5:-Let `quadI = (0, 1)` , be the Borel field of subsets of `quadI` and `mu` is the Lebesgue measure on

. For `quadn = 1, 2,....,` if `quadA_n=(0,1/n), mu(lim "sup" A_n)=`

A:-0

B:-0.5

C:-1

D:-`1/n`

Ans: A

6:-Let `quadW` be the subspace of generated by the vectors (1, -2, 5, -3), (2, 3, 1, -4) and (3, 8, -3, -5). Then

the dimension of `quadW` is

A:-4

B:-3

C:-2

D:-1

Ans: C

7:-For any arbitrary matrices `quadA` and `quadB` , the sum of ranks of `quadA` and `quadB` is always

A:-less than rank `quad(A+B)`

B:-less than or equal to rank`quad(A+B)`

C:-greater than rank`quad(A+B)`

D:-greater than or equal to rank`quad(A+B)`

Ans: D

8:-Let `quadA` and `quadB` are `quadnxxn` square matrices. Then the eigen values of `quadAB` are same as

the eigen values of

A:-`quadA+B`

B:-`quadA-B`

C:-`quadB-A`

D:-`quadBA`

Ans: D

9:-The quadratic polynomial corresponds to the matrix `quadA=((1,0,1/2),(0,0,-1),(1/2,-1,0))` ` ` is

A:-`quadx^2+1/2xz-xy`

B:-`quadx^2-2yz+xz`

C:-`quadx^2+1/2yz-xy`

D:-`quadx^2+yz-2xz`

Ans: B

10:-Let `quadP` be an `quadmxxm` orthogonal matrix, `quadQ` be an `quadnxxn` orthogonal matrix and `quadA`

any `quadmxxn` matrix. If `quadA^T` denote the transpose of `quadA` and `quadA^-` denote the generalized inverse of

`A` , then the generalized inverse of `quadPAQ` is

A:-`quadP^TA^{-}Q^T`

B:-`quadQ^TA^{-}P^T`

C:-`quadPA^{-}Q`

D:-`quadQA^{-}P`

Ans: B

11:-If `quad{A_n}` is a sequence of events on a probability space (Ω,`quadA,P)` such that `quadA_n->A`

as `quadn->oo` , then what is the value of lim`quadP(A_n)` ?

A:-zero

B:-one

C:-`quadP(A)`

D:-need not exist

Ans: C

12:-If `quadA` and `quadB` are mutually exclusive events, each with positive probabilities, then they are

A:-independent events

B:-dependent events

C:-equally likely events

D:-exhaustive events

Ans: B

13:-If `quad{A_n}` is a sequence of events such that `quadsum_(k=1)^ooP(A_k)=oo` , then

`quadP(lim"sup"A_n)=1` provided events are

A:-equally likely

B:-Mutually exclusive

C:-independent

D:-pair-wise mutually exclusive

Ans: C

14:-Let `quad{A_n}` be a sequence of events such that `quadB_1=A_1` and `quadB_k=A^c_1

A^c_2...` `A_{k-1}^c A_k` for `quadk>=2` , in which `quadA^c` is the complement of `quadA` . Then the sequence of

events `quad{B_n}` are

A:-Pair-wise independent

B:-Mutually independent

C:-Mutually dependent

D:-Pair-wise mutually exclusive

Ans: D

15:-If `quadX` is a random variable with finite expectation, then the value of `quadxP(X<-x)` as `quadx->oo` is

A:-infinity

B:-unity

C:-zero

D:-indeterminate

Ans: C

16:-If `quadX` is a symmetric random variable with distribution function `quadF` and real valued characteristic

function Φ, then for any `quadx` in ,`quadF(x)=`

A:-`quadF(-x)`

B:-`quadF(-x-0)`

C:-`quadF(-x-0)-1`

D:-`quad1-F(-x-0)`

Ans: D

17:-If the characteristic function Φ of distribution function `quadF` is absolutely integrable on , then for

any`quadx` in , `quad f'={dF(x)}/dx` is

A:-bounded

B:-uniformly continuous

C:-both (1) and (2)

D:-Neither (1) nor (2)

Ans: C

18:-Let `quadX` and `quadX_n` be independent standard normal variables on a probability space (Ω,`quadfrA,P)` `

`, for `quadn>=1` . Then which of the following is not true?

A:-`X_nstackrel(P)(->)X`

B:-`X_nstackrel(d)(->)X`

C:-`quadE(X_n-X)=0`

D:-`quadVar(X_n-X)=2`

Ans: A

19:-The sequence `quad{X_n}` of independent random variables, each with finite second moment, obeys SLLN if

A:-`quadsum_(k=1)^ooVar(X_k)<oo`

B:-`quadsum_(k=1)^oo{Var(X_k)}/k<oo`

C:-`quadsum_(k=1)^oo{Var(X_k)}/sqrt(k)<oo`

D:-`quadsum_(k=1)^oo{Var(X_k)}/k^2<oo`

Ans: D

20:-Let `quad{X_n}` sequence of independent random variables with

`quadP(X_k=+-k)=1/2k^-Lambda` and `quadP(X_k=0)=1-k^-Lambda` , for `quadk>=1`

Then the sequence does not obey CLT if

A:-`quadLambda=0`

B:-`quadLambda=1`

C:-`quadLambdain(0,1/2)`

D:-`quadLambdain(1/2,1)`

Ans: B

21:-Let `quadX` be a random variable with probability mass function

`quad p(x) = {((6)/(pi^2 x^2) for x=1 ; -2 ; 3 ; -4 ...),(0 elsewhere):}`

Then

A:-`quadE(X)=oo`

B:-`quadE(X)` exists

C:-`quadE(X)<oo` and `quadE(X)` exists

D:-`quadE(X)<oo` , but `quadE(X)` does not exist

Ans: D

22:-Let `quad(X,Y)` has joint density

`quadf(x,y)={(1/8(6-x-y) 0<=x<2; 2<=y<4),(0 "elsewhere"):}`

Then `quadP(X+Y<3)=`

A:-`5/24`

B:-`5/8`

C:-`3/8`

D:-None of these

Ans: A

23:-If `quadX` and `quadY` are two random variables having finite expectations, then the value

of `quadE["min"{X,Y}+"max"{X,Y}]` is

A:-less than `quadE(XY)`

B:-less than `quadE(X+Y)`

C:-equal to `quadE(XY)`

D:-equal to`quadE(X+Y)`

Ans: D

24:-The Poisson distribution `quadP(Lambda)` is unimodal when

A:-`quadlambda` is not an integer

B:-`quadlambda` is an integer

C:-Both (1) and (2)

D:-Neither (1) nor (2)

Ans: A

25:-Which of the following distribution is not a member of power series family of distributions?

A:-Binomial

B:-Poisson

C:-Geometric

D:-Hypergeometric

Ans: D

26:-If `quadX` follows normal `quadN(mu,sigma)` , then the approximate value of `quadE{|X-mu|}` is

A:-Zero

B:-`sigma`

C:-`quad4/5sigma`

D:-`quadsqrt(4/Pi)sigma`

Ans: C

27:-If `quadX` is uniformly distributed with mean unity and variance 0.75, then `quadP(X>1)=`

A:-0.25

B:-0.5

C:-0.75

D:-1

Ans: B

28:-If `quadX` follows normal `quadN(mu,Sigma)` , then `quadY=e^X` follows

A:-Log-normal distribution

B:-Exponential distribution

C:-Logistic distribution

D:-Pareto distribution

Ans: A

29:-If `quadX_j` follows exponential `quadE(Theta_j)` distribution, for `quadj=1,2,...,n,` then the distribution

of `quad"min"{X_1,X_2,...,X_n}`

A:-`quadE(Theta_j)`

B:-` E (prod_{j=1}^n theta_j)`

C:-`quadE(sum_(j=1)^nTheta_j)`

D:-`quadE["min"{Theta_1,Theta_2,...,Theta_n}]`

Ans: C

30:-The mode of `quadF` -distribution is

A:-always less than unity

B:-sometimes less than unity

C:-always greater than unity

D:-sometimes equal to unity

Ans: A

31:-t-test was (student's t-test) was developed by

A:-William Gosset

B:-Fischer

C:-George Snedecor

D:-Karl Pearson

Ans: A

32:-A two dimensional frequency density diagram is

A:-Pie diagram

B:-Histogram

C:-Frequency polygon

D:-Line diagram

Ans: B

`quad p(x) = {((6)/(pi^2 x^2) for x=1 ; -2 ; 3 ; -4 ...),(0 elsewhere):}`

Then

A:-`quadE(X)=oo`

B:-`quadE(X)` exists

C:-`quadE(X)<oo` and `quadE(X)` exists

D:-`quadE(X)<oo` , but `quadE(X)` does not exist

Ans: D

22:-Let `quad(X,Y)` has joint density

`quadf(x,y)={(1/8(6-x-y) 0<=x<2; 2<=y<4),(0 "elsewhere"):}`

Then `quadP(X+Y<3)=`

A:-`5/24`

B:-`5/8`

C:-`3/8`

D:-None of these

Ans: A

23:-If `quadX` and `quadY` are two random variables having finite expectations, then the value

of `quadE["min"{X,Y}+"max"{X,Y}]` is

A:-less than `quadE(XY)`

B:-less than `quadE(X+Y)`

C:-equal to `quadE(XY)`

D:-equal to`quadE(X+Y)`

Ans: D

24:-The Poisson distribution `quadP(Lambda)` is unimodal when

A:-`quadlambda` is not an integer

B:-`quadlambda` is an integer

C:-Both (1) and (2)

D:-Neither (1) nor (2)

Ans: A

25:-Which of the following distribution is not a member of power series family of distributions?

A:-Binomial

B:-Poisson

C:-Geometric

D:-Hypergeometric

Ans: D

26:-If `quadX` follows normal `quadN(mu,sigma)` , then the approximate value of `quadE{|X-mu|}` is

A:-Zero

B:-`sigma`

C:-`quad4/5sigma`

D:-`quadsqrt(4/Pi)sigma`

Ans: C

27:-If `quadX` is uniformly distributed with mean unity and variance 0.75, then `quadP(X>1)=`

A:-0.25

B:-0.5

C:-0.75

D:-1

Ans: B

28:-If `quadX` follows normal `quadN(mu,Sigma)` , then `quadY=e^X` follows

A:-Log-normal distribution

B:-Exponential distribution

C:-Logistic distribution

D:-Pareto distribution

Ans: A

29:-If `quadX_j` follows exponential `quadE(Theta_j)` distribution, for `quadj=1,2,...,n,` then the distribution

of `quad"min"{X_1,X_2,...,X_n}`

A:-`quadE(Theta_j)`

B:-` E (prod_{j=1}^n theta_j)`

C:-`quadE(sum_(j=1)^nTheta_j)`

D:-`quadE["min"{Theta_1,Theta_2,...,Theta_n}]`

Ans: C

30:-The mode of `quadF` -distribution is

A:-always less than unity

B:-sometimes less than unity

C:-always greater than unity

D:-sometimes equal to unity

Ans: A

31:-t-test was (student's t-test) was developed by

A:-William Gosset

B:-Fischer

C:-George Snedecor

D:-Karl Pearson

Ans: A

32:-A two dimensional frequency density diagram is

A:-Pie diagram

B:-Histogram

C:-Frequency polygon

D:-Line diagram

Ans: B

33. Data taken from publication 'agricultural statistics in india ' will be considered as :

1) primary data

2) secondary data

3) both primary data and secondary data

4) none of these.

Ans: 2

34. Which of the following represents data ?

1) a single value

2) only two values in a set

3) different values in a set

4) none of these.

Ans: 3

35. In tabulation source of data, if any, is shown in the

1) body

2) stub

3) foot note

4) caption

Ans: 3

36. Among following statements, which one is correct ?

1) classification follows tabulation

2) classification preceeds tabulation

3) both are done simultaneously

4) no criterion

Ans: 2

37. The relative frequencies in a histogram are proportional to :

1) width of rectangles

2) area of rectangles

3) diagonal length of rectangles

4) height of rectangles

Ans: 4

38. A frequency curve is a limiting form of a

1) histogram

2) frequency polygon

3) both histogram and frequency polygon

4) none of these

Ans: 2

39. Sum of the square of deviations will be least when measured from :

1) zero

2) median

3) mode

4) mean

Ans: 4

40. Which of the following represent median ?

1) first quartile

2) 25th percentile

3) 50th percentile

4) third quartile

Ans: 3

41. To compare the average sale of shirts of different size in two shops the most appropriate measure is :

1) median

2) mean

3) harmonic mean

4) mode

Ans: 4

42. A suitable mean for finding the average of proportions is :

1) arithmetic mean

2) geometric mean

3) harmonic mean

4) weighted mean

Ans: 4

43. Which of the following measure is least affected by sampling fluctuations ?

1) mean

2) mode

3) median

4) hormonic mean

Ans: 1

44. The geometric mean of three observations 40, 50 and x is 10, then the value of x is :

1) 1/2

2) 1

3) 2

4) 4

Ans: 1

45. The mean of 100 students marks was found to be 40. it was found later that a mark 53 was read as 83. the correct mean is :

1) 40.30

2) 40.70

3) 39.40

4) 39.70

Ans: 4

46. The point of intersection of ogive curves corresponds to :

1) arithmetic mean

2) geometric mean

3) median

4) none of these.

Ans: 3

47. If open intervals are presents in a frequency distribution, the most appropriate measure of central tendency is :

1) median

2) arithmetic mean

3) geometric mean

4) harmonic mean

Ans: 1

48. The most appropriate diagram to represent data regarding monthly expenditure is :

1) histogram

2) pie diagram

3) line graph

4) frequency polygon

Ans: 2

49. Which of the following is not a two dimensional diagram ?

1) square diagram

2) multiple bar diagram

3) rectangular diagram

4) pie-diagram

Ans: 2

50. Histogram is suitable for the data :

1) continuous frequency distribution

2) discrete frequency distribution

3) individual series

4) all of these.

Ans: 1

51. From histogram we can easily find the :

1) mean

2) median

3) mode

4) none of these

Ans: 3

52. Pictograms are suitable for the data given in :

1) fractional number

2) whole numbers

3) both fractional number and whole number

4) none of these.

Ans: 2

53. If the harmonic mean of two numbers 'x' and 'y' is 6. if x = 4, then y will be

1) 4

2) 8

3) 10

4) 12

Ans: 1

54. The sample mean of two data sets a and b are equal and then coefficient of variations are respectively 44.8 and 56.0 , what is the ratio of standard deviation of set a to that of set b ?

1) 1/5

2) 4/5

3) 5/4

4) none of these

Ans: 2

55. For some data , mean and variance are given as 25 and 10 . now if all the values given in data are multiplied by 5 then new mean and variance are :

1) 125 , 250

2) 30 , 35

3) 125 , 50

4) none of these.

Ans: 1

56. Which of the following measure is based on all observation of the series :

1) median

2) range

3) quartile deviation

4) standard deviation

Ans: 4

57. A null hypothesis is a :

1) negation hypothesis

2) hypothesis of no difference

3) hypothesis under test for possible rejection

4) all of these.

Ans: 4

58. An alternative hypothesis is one :

1) which is to be rejected.

2) which is to be accepted.

3) against which null hypothesis is tested.

4) none of these

Ans: 3

59. Rejection of null hypothesis when it is true is called :

1) type i error

2) type ii error

3) both i & ii types of errors

4) neither type i nor type ii error

Ans: 1

60. Acceptance of null hypothesis when it is false is known as :

1) type i error

2) type ii error

3) both i & ii types of errors

4) neither type i nor type ii error

Ans: 2

61. Critical region provides basis for :

1) rejection of null hypothesis

2) acceptance of null hypothesis

3) no decision about null hypothesis

4) all of these

Ans: 1

62. The area of critical region depends on :

1) size of type ii error

2) size of type i error

3) value of statistics used

4) size of sample

Ans: 2

63. For testing the independence of two attributes, the degrees of freedom for a chi-square test in a 4 x 3 contingency table is :

1) 12

2) 9

3) 6

4) 8

Ans: 3

64. Who gave the chi-square test of goodness of fit ?

1) r. a. fisher

2) j. neyman

3) karl pearson

4) snedecor

Ans: 3

65. If there are k classes in a chi-square test of goodness of fit. the degrees of freedom of the chi-square are :

1) k

2) k-1

3) 2k

4) 2k-1

Ans: 2

66. Name the factors upon which the domain of survey depends :`

1) objectives

2) availability of time

3) resources

4) all of these

Ans: 4

67. A sampling frame is:

1) method of drawing sample

2) total number of all possible samples

3) list of units of population

4) list of units of sample

Ans: 3

68. Simple random samples can be drawn with the help of :

1) random number table

2) chit method

3) roulette wheel

4) all of these.

Ans: 4

69. In proportional allocation, if the sizes of all strata are equal, it reduces to :

1) neyman allocation

2) equal allocation

3) optimum allocation

4) none of these.

Ans: 2

70. For simple random sampling without replacement the sample mean for estimating population mean is

1) always unbiased estimator

2) may or may not be unbiased estimator

3) always biased estimator

4) none of these.

Ans: 1

71. For proper representation of population in cluster sampling each cluster is further subsampled then the resultant sampling scheme is known as

1) cluster sampling

2) two-stage sampling

3) stratified sampling

4) systematic sampling

Ans: 2

72. Simple random sampling without replacement is superior to simple random sampling with replacement because :

1) it is simple

2) it is easy to get sample

3) it is more efficient

4) none of these

Ans: 3

73. Which of the following is not a probability sampling ?

1) simple random sampling

2) stratified sampling

3) purposive sampling

4) cluster sampling

Ans: 3

74. The allocation providing smallest variance of the estimator under stratified random sampling :

1) arbitrary allocation

2) neyman's allocation

3) equal allocation

4) proportional allocation

Ans: 2

75. Stratified sampling comes under the category of :

1) unrestricted sampling

2) subjective sampling

3) purposive sampling

4) restricted sampling

Ans: 4

76. A population is divided into three strata consisting of 16, 24 & 60 units respectively. if a sample of size 25 is to be selected, the number of units drawn from each strata with proportional allocation is :

1) 6, 4, 15

2) 4, 6, 15

3) 8, 8, 9

4) 4, 8, 13

Ans: 2

77. Regarding appropriate number of strata which statement is true ?

1) lesser the number of strata better it is

2) larger the number of strata poorer it is

3) larger the number of strata better it is

4) not more than 10 items should be there in each strata

Ans: 3

78. Cluster sampling in practice is used when :

1) sampling frame of last stage unit is not known

2) sampling units are well arranged

3) both sampling frame of last stage unit is not known and sampling units are well arranged

4) none of these.

Ans: 1

79. As the sample size increases, the chances of human bias are minimised in case of

1) simple random sampling

2) stratified sampling

3) systematic sampling

4) purposive sampling

Ans: 4

80. Out of the following, the variances of sample mean can not be estimated unbiasedly for

1) simple random sampling

2) stratified random sampling

3) systematic sampling

4) none of these.

Ans: 3

81. In respect of chi-square distribution , which one of the following is true ?

1) mean > variance

2) mean < variance

3) mean = variance

4) nothing can be said

Ans: 2

82. The error arises when we are examining only a part of population is known as :

1) non-sampling error

2) sampling error

3) both non-sampling error and sampling error

4) none of these

Ans: 2

83. In stratified random sampling if the variances of all the strata are equal then neyman allocation reduces to :

1) optimum allocation

2) equal allocation

3) proportional allocation

4) none of these.

Ans: 3

1) primary data

2) secondary data

3) both primary data and secondary data

4) none of these.

Ans: 2

34. Which of the following represents data ?

1) a single value

2) only two values in a set

3) different values in a set

4) none of these.

Ans: 3

35. In tabulation source of data, if any, is shown in the

1) body

2) stub

3) foot note

4) caption

Ans: 3

36. Among following statements, which one is correct ?

1) classification follows tabulation

2) classification preceeds tabulation

3) both are done simultaneously

4) no criterion

Ans: 2

37. The relative frequencies in a histogram are proportional to :

1) width of rectangles

2) area of rectangles

3) diagonal length of rectangles

4) height of rectangles

Ans: 4

38. A frequency curve is a limiting form of a

1) histogram

2) frequency polygon

3) both histogram and frequency polygon

4) none of these

Ans: 2

39. Sum of the square of deviations will be least when measured from :

1) zero

2) median

3) mode

4) mean

Ans: 4

40. Which of the following represent median ?

1) first quartile

2) 25th percentile

3) 50th percentile

4) third quartile

Ans: 3

41. To compare the average sale of shirts of different size in two shops the most appropriate measure is :

1) median

2) mean

3) harmonic mean

4) mode

Ans: 4

42. A suitable mean for finding the average of proportions is :

1) arithmetic mean

2) geometric mean

3) harmonic mean

4) weighted mean

Ans: 4

43. Which of the following measure is least affected by sampling fluctuations ?

1) mean

2) mode

3) median

4) hormonic mean

Ans: 1

44. The geometric mean of three observations 40, 50 and x is 10, then the value of x is :

1) 1/2

2) 1

3) 2

4) 4

Ans: 1

45. The mean of 100 students marks was found to be 40. it was found later that a mark 53 was read as 83. the correct mean is :

1) 40.30

2) 40.70

3) 39.40

4) 39.70

Ans: 4

46. The point of intersection of ogive curves corresponds to :

1) arithmetic mean

2) geometric mean

3) median

4) none of these.

Ans: 3

47. If open intervals are presents in a frequency distribution, the most appropriate measure of central tendency is :

1) median

2) arithmetic mean

3) geometric mean

4) harmonic mean

Ans: 1

48. The most appropriate diagram to represent data regarding monthly expenditure is :

1) histogram

2) pie diagram

3) line graph

4) frequency polygon

Ans: 2

49. Which of the following is not a two dimensional diagram ?

1) square diagram

2) multiple bar diagram

3) rectangular diagram

4) pie-diagram

Ans: 2

50. Histogram is suitable for the data :

1) continuous frequency distribution

2) discrete frequency distribution

3) individual series

4) all of these.

Ans: 1

51. From histogram we can easily find the :

1) mean

2) median

3) mode

4) none of these

Ans: 3

52. Pictograms are suitable for the data given in :

1) fractional number

2) whole numbers

3) both fractional number and whole number

4) none of these.

Ans: 2

53. If the harmonic mean of two numbers 'x' and 'y' is 6. if x = 4, then y will be

1) 4

2) 8

3) 10

4) 12

Ans: 1

54. The sample mean of two data sets a and b are equal and then coefficient of variations are respectively 44.8 and 56.0 , what is the ratio of standard deviation of set a to that of set b ?

1) 1/5

2) 4/5

3) 5/4

4) none of these

Ans: 2

55. For some data , mean and variance are given as 25 and 10 . now if all the values given in data are multiplied by 5 then new mean and variance are :

1) 125 , 250

2) 30 , 35

3) 125 , 50

4) none of these.

Ans: 1

56. Which of the following measure is based on all observation of the series :

1) median

2) range

3) quartile deviation

4) standard deviation

Ans: 4

57. A null hypothesis is a :

1) negation hypothesis

2) hypothesis of no difference

3) hypothesis under test for possible rejection

4) all of these.

Ans: 4

58. An alternative hypothesis is one :

1) which is to be rejected.

2) which is to be accepted.

3) against which null hypothesis is tested.

4) none of these

Ans: 3

59. Rejection of null hypothesis when it is true is called :

1) type i error

2) type ii error

3) both i & ii types of errors

4) neither type i nor type ii error

Ans: 1

60. Acceptance of null hypothesis when it is false is known as :

1) type i error

2) type ii error

3) both i & ii types of errors

4) neither type i nor type ii error

Ans: 2

61. Critical region provides basis for :

1) rejection of null hypothesis

2) acceptance of null hypothesis

3) no decision about null hypothesis

4) all of these

Ans: 1

62. The area of critical region depends on :

1) size of type ii error

2) size of type i error

3) value of statistics used

4) size of sample

Ans: 2

63. For testing the independence of two attributes, the degrees of freedom for a chi-square test in a 4 x 3 contingency table is :

1) 12

2) 9

3) 6

4) 8

Ans: 3

64. Who gave the chi-square test of goodness of fit ?

1) r. a. fisher

2) j. neyman

3) karl pearson

4) snedecor

Ans: 3

65. If there are k classes in a chi-square test of goodness of fit. the degrees of freedom of the chi-square are :

1) k

2) k-1

3) 2k

4) 2k-1

Ans: 2

66. Name the factors upon which the domain of survey depends :`

1) objectives

2) availability of time

3) resources

4) all of these

Ans: 4

67. A sampling frame is:

1) method of drawing sample

2) total number of all possible samples

3) list of units of population

4) list of units of sample

Ans: 3

68. Simple random samples can be drawn with the help of :

1) random number table

2) chit method

3) roulette wheel

4) all of these.

Ans: 4

69. In proportional allocation, if the sizes of all strata are equal, it reduces to :

1) neyman allocation

2) equal allocation

3) optimum allocation

4) none of these.

Ans: 2

70. For simple random sampling without replacement the sample mean for estimating population mean is

1) always unbiased estimator

2) may or may not be unbiased estimator

3) always biased estimator

4) none of these.

Ans: 1

71. For proper representation of population in cluster sampling each cluster is further subsampled then the resultant sampling scheme is known as

1) cluster sampling

2) two-stage sampling

3) stratified sampling

4) systematic sampling

Ans: 2

72. Simple random sampling without replacement is superior to simple random sampling with replacement because :

1) it is simple

2) it is easy to get sample

3) it is more efficient

4) none of these

Ans: 3

73. Which of the following is not a probability sampling ?

1) simple random sampling

2) stratified sampling

3) purposive sampling

4) cluster sampling

Ans: 3

74. The allocation providing smallest variance of the estimator under stratified random sampling :

1) arbitrary allocation

2) neyman's allocation

3) equal allocation

4) proportional allocation

Ans: 2

75. Stratified sampling comes under the category of :

1) unrestricted sampling

2) subjective sampling

3) purposive sampling

4) restricted sampling

Ans: 4

76. A population is divided into three strata consisting of 16, 24 & 60 units respectively. if a sample of size 25 is to be selected, the number of units drawn from each strata with proportional allocation is :

1) 6, 4, 15

2) 4, 6, 15

3) 8, 8, 9

4) 4, 8, 13

Ans: 2

77. Regarding appropriate number of strata which statement is true ?

1) lesser the number of strata better it is

2) larger the number of strata poorer it is

3) larger the number of strata better it is

4) not more than 10 items should be there in each strata

Ans: 3

78. Cluster sampling in practice is used when :

1) sampling frame of last stage unit is not known

2) sampling units are well arranged

3) both sampling frame of last stage unit is not known and sampling units are well arranged

4) none of these.

Ans: 1

79. As the sample size increases, the chances of human bias are minimised in case of

1) simple random sampling

2) stratified sampling

3) systematic sampling

4) purposive sampling

Ans: 4

80. Out of the following, the variances of sample mean can not be estimated unbiasedly for

1) simple random sampling

2) stratified random sampling

3) systematic sampling

4) none of these.

Ans: 3

81. In respect of chi-square distribution , which one of the following is true ?

1) mean > variance

2) mean < variance

3) mean = variance

4) nothing can be said

Ans: 2

82. The error arises when we are examining only a part of population is known as :

1) non-sampling error

2) sampling error

3) both non-sampling error and sampling error

4) none of these

Ans: 2

83. In stratified random sampling if the variances of all the strata are equal then neyman allocation reduces to :

1) optimum allocation

2) equal allocation

3) proportional allocation

4) none of these.

Ans: 3

84. The chances of passing a congenital defect A by affected parents to their children is 0.15. They plan to have 2 children. What is the probability of both the children having the genetic disease ?

(A) 0.3 (B) 0.45 (C) 0.0225 (D) 0.225

Ans: C

85. The odds of an event occurring is 5. What is the probability of that event occurring ?

(A) 0.83 (B) 0.75 (C) 0.2 (D) 0.05

Ans: A

86. When the relative deviate in a standard normal curve is −2 the proportion of area from the middle of the curve to the designated value is :

(A) 34.1% (B) 47.7% (C) 68.2% (D) 95.4%

Ans: B

87. When mean of a distribution is 85 and median is 98 the distribution is :

(A) Symmetrical (B) Positively Skewed (C) Negatively Skewed (D) SD needed to find out Skewedness

Ans: C

88. Likert scale is :

(A) Nominal scale (B) Ordinal scale (C) Interval scale (D) Ratio scale

Ans: B

89. Among the following which is the demerit of Arithmetic Mean

A) It has the simplest formula to calculate and easily understood

B) The extreme values have greater effect on mean

C) It is least affected by sampling fluctuation

D) The same result will come on repeated calculations

Ans: B

(A) 0.3 (B) 0.45 (C) 0.0225 (D) 0.225

Ans: C

85. The odds of an event occurring is 5. What is the probability of that event occurring ?

(A) 0.83 (B) 0.75 (C) 0.2 (D) 0.05

Ans: A

86. When the relative deviate in a standard normal curve is −2 the proportion of area from the middle of the curve to the designated value is :

(A) 34.1% (B) 47.7% (C) 68.2% (D) 95.4%

Ans: B

87. When mean of a distribution is 85 and median is 98 the distribution is :

(A) Symmetrical (B) Positively Skewed (C) Negatively Skewed (D) SD needed to find out Skewedness

Ans: C

88. Likert scale is :

(A) Nominal scale (B) Ordinal scale (C) Interval scale (D) Ratio scale

Ans: B

89. Among the following which is the demerit of Arithmetic Mean

A) It has the simplest formula to calculate and easily understood

B) The extreme values have greater effect on mean

C) It is least affected by sampling fluctuation

D) The same result will come on repeated calculations

Ans: B

90:-Suppose a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four from B and five from manufacturer C. The cost of maintaining each truck was recorded. The company used ANOVA to test if the mean maintenance cost of the trucks from each manufacturer were equal. To apply the F test, how many degrees of freedom are in the denominator ?

A:-2

B:-3

C:-11

D:-14

Ans: C

91:-The chi-square distribution can assume

A:-Only positive values

B:-Only negative values

C:-Negative and positive values or zero

D:-Only zero

Ans: A

92:-A regression equation was computed to be Y = 35 + 6X. The value of the 35 indicates that

A:-A regression line crosses the Y axis at 35

B:-The coefficient of correlation is 35

C:-The coefficient of determination is 35

D:-An increase of one unit of X will result in an increase of 35 in Y

Ans: A

93:-Until this year the mean braking distance of a Nikton automobile moving at 60 miles per hour was 175 feet. Nikton engineers have developed what they consider a better braking system. They test the new brake system on a random sample of 64 cars and determine the sample mean braking distance x = 167 feet (assume the population standard deviation is known to be 32 feet). How many cars should be tested if Nikton wants to be 95% confident of being within 1 foot of the population mean braking distance ?

A:-4194

B:-3934

C:-3216

D:-3016

Ans: B

94:-When carrying out a large sample test of `H_(0)` : `mu` 10 vs. `H_(a)` : `mu` ``> 10 by using a critical value, we reject `H_(0)` at level of significance `alpha` when the calculated test statistic is

A:-Less than `z_(alpha)`

B:-Less than `-z_(alpha)`

C:-Greater than `z_(alpha/2)` ``

D:-Greater than `z_(alpha)`

Ans: D

95:-If the standard deviation of a set of scores is 7.5, what would the value of the standard deviation become if 5 points were added to every score in the set ?

A:-37.5

B:-12.5

C:-Cannot be determined without further information

D:-Stay the same

Ans: D

96:-The distribution of salaries for most business is known to be skewed to the right or positively skewed. Which of the following would be the BEST measure to determine the location of the center of the distribution ?

A:-Variance

B:-Median

C:-Mode

D:-Mean

Ans: B

97:-According to a recent survey approximately 25% of all college students work full time (that is, there is 0.25 probability for any given student to work full time). If the random variable X represents the number of students who work full time in samples of size 10, what is the expected value of X ?

A:-2.0

B:-2.5

C:-3.0

D:-More information is needed

Ans: B

98:-To determine if a diet supplement is useful for increasing weight, patients are weighed at the start of the program and at the end of the program. This is an example of a(n)

A:-Test of paired differences

B:-Independent sample

C:-One-sample test for means

D:-Two-sample test for means

Ans: A

99:-Suppose we are testing the difference between two proportions at the 0.05 level of significance. If the computed Z is -1.07, what is our decision ?

A:-Reject the null hypothesis

B:-Do not reject the null hypothesis

C:-Take a larger sample

D:-Reserve judgement

Ans: B

100:-Using two independent samples, two population means are compared to determine if a difference exists. The number in the sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical value ?

A:-24

B:-25

C:-26

D:-27

Ans: B

A:-2

B:-3

C:-11

D:-14

Ans: C

91:-The chi-square distribution can assume

A:-Only positive values

B:-Only negative values

C:-Negative and positive values or zero

D:-Only zero

Ans: A

92:-A regression equation was computed to be Y = 35 + 6X. The value of the 35 indicates that

A:-A regression line crosses the Y axis at 35

B:-The coefficient of correlation is 35

C:-The coefficient of determination is 35

D:-An increase of one unit of X will result in an increase of 35 in Y

Ans: A

93:-Until this year the mean braking distance of a Nikton automobile moving at 60 miles per hour was 175 feet. Nikton engineers have developed what they consider a better braking system. They test the new brake system on a random sample of 64 cars and determine the sample mean braking distance x = 167 feet (assume the population standard deviation is known to be 32 feet). How many cars should be tested if Nikton wants to be 95% confident of being within 1 foot of the population mean braking distance ?

A:-4194

B:-3934

C:-3216

D:-3016

Ans: B

94:-When carrying out a large sample test of `H_(0)` : `mu` 10 vs. `H_(a)` : `mu` ``> 10 by using a critical value, we reject `H_(0)` at level of significance `alpha` when the calculated test statistic is

A:-Less than `z_(alpha)`

B:-Less than `-z_(alpha)`

C:-Greater than `z_(alpha/2)` ``

D:-Greater than `z_(alpha)`

Ans: D

95:-If the standard deviation of a set of scores is 7.5, what would the value of the standard deviation become if 5 points were added to every score in the set ?

A:-37.5

B:-12.5

C:-Cannot be determined without further information

D:-Stay the same

Ans: D

96:-The distribution of salaries for most business is known to be skewed to the right or positively skewed. Which of the following would be the BEST measure to determine the location of the center of the distribution ?

A:-Variance

B:-Median

C:-Mode

D:-Mean

Ans: B

97:-According to a recent survey approximately 25% of all college students work full time (that is, there is 0.25 probability for any given student to work full time). If the random variable X represents the number of students who work full time in samples of size 10, what is the expected value of X ?

A:-2.0

B:-2.5

C:-3.0

D:-More information is needed

Ans: B

98:-To determine if a diet supplement is useful for increasing weight, patients are weighed at the start of the program and at the end of the program. This is an example of a(n)

A:-Test of paired differences

B:-Independent sample

C:-One-sample test for means

D:-Two-sample test for means

Ans: A

99:-Suppose we are testing the difference between two proportions at the 0.05 level of significance. If the computed Z is -1.07, what is our decision ?

A:-Reject the null hypothesis

B:-Do not reject the null hypothesis

C:-Take a larger sample

D:-Reserve judgement

Ans: B

100:-Using two independent samples, two population means are compared to determine if a difference exists. The number in the sample is fifteen and the number in the second sample is twelve. How many degrees of freedom are associated with the critical value ?

A:-24

B:-25

C:-26

D:-27

Ans: B