Odisha CPET 2022 Question Paper Statics

ODISHA
CPET

QUESTION PAPER
2022
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COMMON P.G. ENTRANCE TEST–2022 (CPET-2022)

Subject Code : 46 Test Booklet No.:

Entrance Subject : Statistics Hall Ticket No.:

TEST BOOKLET

Time Allowed : 90 Minutes Full Marks : 70

INSTRUCTIONS TO CANDIDATES
1. Please do not open this Question Booklet until asked to do so.
2. Check the completeness of the Question Booklet immediately after opening.
3. Enter your Hall Ticket No. on the Test Booklet in the box provided alongside. Do not write
anything else on the Test Booklet.

up Test Booklet Serial No. & OMR Answer Sheet Serial No. in the Attendance Sheet carefully.

5. Each question has four answer options marked (A), (B), (C) & (D).
6. Answers are to be marked on the Answer Sheet, which is provided separately.
7. Choose the most appropriate answer option and darken the oval completely, corresponding to
(A), (B), (C) or (D) against the relevant question number.
8. Use only Blue/Black Ball Point Pen to darken the oval for answering.
9. Please do not darken more than one oval against any question, as scanner will read such markings
as wrong answer.
10. Each question carries equal marks. There will be no negative marking for wrong answer.
11. Electronic items such as calculator, mobile, etc., are not permitted inside the
examination hall.
12. Don’t leave the examination hall until the test is over and permitted by the invigilator.
13. The candidate is required to handover the original OMR sheet to the invigilator and
take the question booklet along with the candidate’s copy of OMR sheet after completion
of the test.
14. Sheet for rough work is appended in the Test Booklet at the end.

W-Statistics-46 P.T.O.

1. The point of intersection of the less than and the greater than Ogive corresponds to:

(A) the median

(B) the mean

(C) the mode

2. Which of the following series represents a ratio scale?

(A) 1,2,3,5,8…..

(B) 1,2,4,8,16,32,64…..

(C) 1,3,5,7,9,11,13……..

(D) 2,4,6,8,10,12,14……

3. The most stable measure of central tendency is

(A) the mean

(B) the median

(C) the mode

4. 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) positively skewed

(C) negatively skewed

(D) Normal

(A) cannot be positive

(B) cannot be negative

(C) is always positive

(D) can be both positive and negative

W-Statistics-46 2

6. In the least square linear trend equation Yt = a + bx, If b is positive, it indicates

(A) rising trend

(B) declining trend

(C) no trend at all

(D) All of these

of association) would be

(A) zero

(B) -0.9

(C) -1

(D) +1

8. In the simultaneous tossing of two perfect coins, the probability of getting at least
one head is :

(A) /2
1

(B) /4
1

(C) 3 4
/
(D) 1

9. A problem in statistics is given to three students whose chances of solving it are 1/2,
1/3 and 14. Then the probability that the problem will be solved is:

(A) 1
/2
(B) 1

(C) 1
/4
(D) 3
/4
10. Two six-faced unbiased dice are thrown. The probability that the sum of the numbers
shown is 7 or their product is 12 is:

(A) 1
/9
(B) 2
/9
(C) 5
/18
W-Statistics-46 3 P.T.O.

11. A bag contains 5 white and 3 black balls. Two balls are drawn at random one after
the other without replacement. The probability that both the balls drawn are black
is:

(A) 2
/7
(B) 3
/8
(C) 3
/28

12. A coin is tossed until a tail appears. Then the expectation of the number of tosses is:

(A) 2

(B) 4

(C) 6

(D) 8

13. The moment generating function of Binomial distribution is

(A) (q + pet)

(B) (q + pet)n

(C) (qet + p)

(D) (qet + p)n

14. In the case of Poisson distribution

(A) The mean is greater than variance

(B) The variance is greater than mean

(C) The mean is equal to variance

15. The size of the critical region is same as

(A) Power of the test

(B) Type I error

(C) Type II error

(D) none of these

W-Statistics-46 4

16. Let x1 , x2 ………. Xn be a random sample from ( µ, 2

limits for µ when 2
is known are

(a )

(B)

(C)

17. The range of z2 variate is

(A) 0 to 1

(D) – 1 to 1

18. To test H0 : 2
= 0
2
against the alternative H1 : 2
< 02 we have

(A) a left-tailed test

(B) a right-tailed test

(C) a two tailed test

(D) none of these

(A) 2
test

(B) F test

(C) t test

20. In the sign test, it is assumed that

(A) the samples are independent

(B) the samples are dependent

(C) the samples have same mean

W-Statistics-46 5 P.T.O.

21. R.B.D is more e

(A) never true

(B) sometimes true

(C) always true

(D) none of these

(A) G/N

(B) G2/N

(C) G/N2

Where G is the Grand Total of all the observed values and N is the total number of
observations.

23. The most important factors causing seasonal variations are

(A) change in fashion

(B) growth of population

(C) Technological improvements

(D) Weather and social customs

24. Which component of time series is mainly applicable in the case of fall in death rate

(A) secular trend

(B) seasonal

(C) cyclic

25. Paasche’s price index is based on

(A) base year quantities

(B) current year quantities

(C) both of them

(D) none of these

W-Statistics-46 6

26. Fi

(A) Time reversal test

(B) Factor reversal test

(C) both of them

27. The lower control limit for p-chart is

(A) E(p) – SE(p)

(B) E(p) – 3 SE (p)

(C) E(p) + 3 SE(p)

(D) E(p) + SE (p)

28. C-chart is used normally when the quality of product is

(A) discrete variable

(B) a continuous variable

(C) both (A) and (B)

(D) none of these

29. If gross reproduction rate is more than 1, it indicates

(A) population would decrease

(B) population would increase

(C) neither increase or decrease

(D) none of these

30. Demography is the systematic study of

(A) Statistics

(B) Population

(C) Culture

(D) Economics

W-Statistics-46 7 P.T.O.

(A) unit of measurement

(B) no unit of measurement

(C) square of the unit of measurement

(D) none of these

32. The sum of absolute deviations about median is

(A) zero

(B) equal

(C) least

(D) greatest

(B) equal to unity

(C) less than unity

(D) equal to zero

34. The normal distribution is a limiting case of Poisson distribution when

(A) 0

(B)

(C)

(D) 1

35. If a,b,c are randomly chosen between 0 and 1, the probability that the quadratic
equation ax2+bx+c = 0 has real roots is

(A) /9
1

(B) /9
8

(C) 2
/9
(D) 4
/9

W-Statistics-46 8

36. If X is a standard normal variable , then X2 / 2 is a

(A) Gamma variable with parameter ½

(B) a normal variate

(C) a poisson variate

(D) none of this

37. 2
distribution is

(A) continuous

(B) multimodal

(C) symmetrical

(D) none of these

38. F distribution is

(A) positively skewed

(B) negatively skewed

(C) having skewness zero

(D) none of these

39. The maximum value for the power of a test is

(A) zero

(C) one

(D) none of these

40. A simple regression estimate is a biased one. The statement

(A) is always true

(B) sometimes true

(C) never true

(D) none of these

W-Statistics-46 9 P.T.O.

41. The bias in the case of a ratio estimate

(A) decreases as the sample size increases

(B) increases as the sample size increases

(C) constantas the sample size increases

(D) none of these

stratum, the larger the sample from that stratum. The statement is

(A) always true

(B) sometimes true

(C) never true

(D) none of these

43. SPRT terminates with probability

(A) half

(B) zero

(C) one

(D) none of these

44. A maximum likelihood estimate is

(A) always biased

(B) always unbiased

(C) sometimes biased

(D) none of these

45. Likelihood ratio test is consistent. The statement is

(A) always true

(B) sometimes true

(C) never true

(D) none of these

W-Statistics-46 10

(A)

(B)

(C)

47. A BIBD is said to be symmetric if

(A) b = and r = k

(B) b = r and =k

(C) b = k and =r

48. In a 23 factorial experiment in blocks of 4 plots involving 3 fertilisers N, P and K,
each at 2 levels the number of degrees of freedom for E.S.S. is

(A) 10

(B) 11

(C) 12

49. If X ~ N (µ, ), then Y=CX ( C non singular) is distributed according to

(A) N ( Cµ, )

(B) N ( Cµ, C C’)

(C) N (µ, C C’)

50. To test the randomness of a given set of observations, the appropriate test is

(A) U test

(B) median test

(C) sign test

(D) run test

W-Statistics-46 11 P.T.O.

t test is

(A) less than 0.864

(B) greater than 0.864

(C) greater than equal to 0.864

52. The control chart used for the fraction of defective items in a sample is

(A) Range chart

(B) X chart

(C) P-chart

(D) C-chart

53. The maximum value of the average outgoing quality for all possible values of
proportion defective is called

(A) Average Outgoing quality (AOQ)

(B) Acceptable Quality Level (AQL)

(C) Average Outgoing Quality Limit (AOQL)

(D) Lot tolerance proportion defective (LTPD)

54. An OC curve is a plot between

(A) Consumer’s risk and Producer’s risk

(B) Probability of acceptance and probability of rejection

(C) Percentage of defective and Probability of acceptance

(D) Average outgoing quality and Probability of acceptance

55. Which one is true regarding residuals in regression analysis?

(A) mean of residuals is always zero

(B) mean of residuals is less than zero

(C) mean of residuals is greater than zero

(D) none of these

W-Statistics-46 12

56. In one way ANOVA, which of the following is used within the F-ratio as a measurement
of the variable of individual observation?

(A) SSE

(B) MSE

(C) MST

(D) none of the above

57. Which of the following theorem is utilised to justify the normality assumption of
random variable in regression model?

(A) Euler’s theorem

(B) Chebyshev’s theorem

(C) Gauss Markov Theorem

(D) Central limit theorem

58. In a Markov transition matrix, the sum of the elements in each row is equal to

(A) 0
1
(B) /2

(C) 1

59. The interval between two successive occurrences of Poisson process {N( t)} having
parameter has a negative exponential distribution with mean

(A)

(B)
1
(C) /

in a string in C

(A) strnchar( )

(B) strchar( )

(C) strrchar( )

(D) strrchr( )
W-Statistics-46 13 P.T.O.

61. A do-while loop is useful when we want that the statements within the loop must be
executed;

(A) at least once

(B) only once

(C) more than once

(D) none of these

62. The 6 x 6 matrix with all entries 1 have rank

(A) 1

(B) 2

(C) 4

(D) 6

63. Let A be 5 x 7 matrix with rank 4. The dimension of the solution space of AX=0 is

(A) 4

(B) 3

(C) 5

(D) 1

64. The dimension of the zero vector space is

(B) 1

(C) 0

65. Find the minimum value of the function f(x) = x2-x+2
1
(A) /2
3
(B) /4
7
(C) /4
1
(D) /4

W-Statistics-46 14

66. The solution of differential equation dy = (4+ y2) dx is

(A) y = 2 tan (x + c )

(B) y = 2 tan (2x + c )

(C) 2y = tan ( x + c )

(D) 2y = 2 tan (x + c )

67. The value of the integral is

(A) 10

(B) 12

(C) 24

68. Considering four sub intervals, the value of by trapezoidal rule is

(A) 0.6870

(B) 0.6950

(C) 0.6677

(D) 0.3597

69. The series converges for

(A) -2 < x < 2

(B) -1 < x < 3

(C) -3 < x < 1

(D) x < 3

70. The value of is

(A) 0

(B) 1

*****

W-Statistics-46 15 P.T.O.

ROUGH WORK

W-Statistics-46 16