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ROUGH WORK

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Objective Multiple Choice Questions
1. If the distribution is moderately symmetrical the relation between mean, median, mode is

Mode 3 Median 2 Mean Mean 3 Median Mode


Mode 3 Mean 2 Median Mean Median 2 (Mean Mode)


2. A person goes from his house to his college at a speed of 60 km/hour and back from his college to house at a speed of 40 km/hour, then his average speed is

50 km/hour 48 km/hour


48.5 km/hour 48.98 km/hour


3. For the mid-values of class intervals given as
25, 34, 43, 52, 61, 70.
The first class of the distribution is


24.5—25.5 24—26


20—30 20.5—29.5


4. The following frequency distribution
Classes Frequency
0—15 25
0—10 10
0—5 04

is classified as

cumulative distribution in less than type


cumulative distribution in more than type


discrete frequency distribution


cumulative frequency distribution


5. The probability of drawing any one diamond card from a pack of playing cards is
1 1







52 13
4 1
13 4
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6. In tossing of two perfect dice, the probability of getting 4 as the sum of the numbers on faces is
4 1

36 12
32


12 12
7. If A and B are any two events and are not disjoint then

P(A . P(A . P(A n


P(A . · P(A . P(A n


8. A problem of statistics is given to 3 students C whose chances of solving the problem
13 1

are and respectively. Then probability that the problem will be solved is
24 4
33


32 2
29 5

32 10
9. The probability of the simultaneous occurrence of two events A and A i.e. P(An is
1212
equal to
· ·
112 221
· All the above
10. An urn contains 5 white and 5 black balls, 4 balls are drawn from the urn, then probability that all 4 balls drawn are black is
4 1

10 2
14


42 5
11. Suppose 5 men out of 100 and 25 women out of 10000 are colour-blind. A colour-blind person is choosen at random. Assuming male and female are equal in number, the probability of choosen person being male is
1 1

20 2020
1 20


30 21
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12. Variance of the mean of a random sample of size if variance is denoted by s2 is equal to
s2 s2

2 n
s2
2
ns n

11 1
13. If P(A n then P(A . is equal to
34 12
7 1

12 12
1 2

2 3
14. In a binomial distribution, mean is 4 and variance is given as then its mode will be
12
4 3·3
15. If mean is denoted by µ and variance by s2, then in a binomial distribution

µ s2 µ s2


µ s2 µ s


16. The distribution for which moment generating function (m.g.f.) does not exist is

Cauchy's distribution Gamma distribution


Exponential distribution Rectangular distribution


17. Gamma variate assumes all values in between the interval

to 8 to 0


0 to 8 0 to 1


18. If the distribution function of two dimensional random variates X and Y is denoted by then

1 0 1


8 0 8


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19. The Normal distribution is a limiting form of Binomial distribution if

n . p . n n . p . 0


n . p . q n . neither p nor q is small


20. The square of a standard normal variate is a

Normal variate Chi-square variate


Poisson variate F variate


21. If each observation of a set is divided by 2 then the mean of new values

Is decreased by 2 Is two times the original mean


Is half of the original mean Remains the same


22. The mean of the squares of first-eleven natural numbers is

33 46
23. In a class 40 students out of 50 passed with mean marks 6.0 and the overall average of class marks is 5.5, then the average marks of failed students is

3.5 2.5


4.0 0.5


24. If each values of a series is multiplied by 10, then coefficient of variation will be increased by

10 percent 5 percent


20 percent 0 percent


25. If for a distribution, coefficient of Kurtosis r2 then the frequency curve is

Platykurtic Leptokurtic


Mesokurtic None


26. The correct relationship between Arithmetic Mean Geometric Mean and Harmonic Mean is

AM GM HM GM AM HM


HM GM AM AM GM HM


27. The average age of 29 students in a class is 20 years. When the age of the class teacher is included, the average is increased by one year. Then the age of the class teacher is

50 years 55 years


49 years 21 years


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28. The sum of n observations is 630 and their mean is 42, then the value of n is

30 15


20 21


29. Mean deviation is minimum when deviations are taken from

Mean Median


Mode Zero


30. If in a skewed distribution mean is 30 and mode is 36, then median of the distribution is

32 28


33 35


31. Two regression coefficients are

Independent of change of origin but not of scale


Dependent of change of origin but not of scale


Independent of change of origin and scale


Dependent of change of origin and scale


32. Both the regression lines of X on Y and Y on X are

Always parallel to each other Intersect each other


Never intersect Always perpendicular


33. If one of the regression coefficient is greater than 1 the other must be

equal to 1 greater than 1


less than 1 less than or equal to 1


34. If the two variables are uncorrected, then the two lines of regression are

perpendicular coincides


parallel does not intersect


35. The two lines of regressions are given as X 2Y 5 0 and 2X 3Y 8. Then the mean values of X and Y respectively are

1 5


3 2


36. Two lines of regression intersect at the point







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37. If a constant 20 is subtracted from each of the values of X and the regression coefficient will be
1

reduced by 20 th of the original value


increased by 20 not changed


20
38. The value of correlation ratio varies from

to 1 to 0


0 to 1 0 to


1
2
39. If the regression line of Y on X is Y aX b and X on Y is X cY the correlation coefficient between X and Y is

a/c
a/d


ac bd


40. If the sum of squares of differences between ten ranks of two series is 33, then the rank correlation coefficient is

.303 .80


.33 .66


41. H0 µ1 µ2 for samples of sizes 8 and 10 from normal populations (variance unknown) would be tested using

Student's t .2 test


Fisher's Z S.N.V.Z. test


42. Students distribution was discovered by

Fisher W.S. Gosset


Karl Pearson Laplace


43. The relation between .2 with n d.f. is

2 mean variance mean 2 variance

mean variance mean2
variance


44. If n the sample size is larger than 30, the Student's t-distribution tends to

F-distribution Cauchy distribution


Chi-square Normal


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45. The range of F-variate is

to 8 0 to 1


0 to 8 to 0


46. F-distribution curve is

Positively skewed Negatively skewed


Symmetrical May be of any shape


47. Mode of the Chi-square distribution with n d.f. lies at the point

.2 n 2 .2 n 1


.2 n .2 n2 1


48. If the sample size n the Students t-distribution reduces to

Normal distribution F-distribution


Cauchy distribution Gamma distribution


49. If X1 and X2 are two independent .2-variate then which of the following has also .2-distribution
X1 X1

X X X
1 2 2
X2
X1 X
X1 2
50. The distribution of .21 is equivalent to the distribution

F1, 8 F1, 0


F8, 1 F1, 1


51. If an estimator T n of population parameter . converges in probability to . as n tends 8 is said to be

unbiased consistent


efficient sufficient


52. An estimator .ˆ is said to be unbiased estimator of . if

.ˆ





2 2
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53. Mean square error of an estimator Tn of . is expressed as

bias var bias var


bias2 var [bias var Tn]2


54. If .ˆ1 and .ˆ 2 are two unbiased estimator of the parameter then .ˆ1 is said to be minimum variance unbiased estimator of . if
V(.ˆ
12 12
V(.ˆ
12 12
55. If T1 and T2 two minimum variance unbiased estimator of then
T T. T
1 2 12
T T T
1 2 12
56. Let X1, X2, ....., Xn be a random sample from Bernoulli population with parameter 0 p then sufficient statistics for this family of distributions is
nn
Xi Xi2

. .
i=1 i=1
n 1n
. Xi . Xi
i=1 i=1
57. Let X1, X2, X3 ........, Xn be a random sample from s2). Then sufficient estimator for s2 is
n n
. Xi . Xi2
i=1 i=1
1n
. Xi
n
i=1
58. For random sampling from s2) the maximum likelihood estimator for µ when s2 is known is
n 1n
. Xi . Xi
n
i=1 i=1
n 1n
. Xi2(D) . Xi2
n
i=1 i=1
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59. If sample mean is x and population mean is µ. Then the most-efficient estimator of µ is
1n n
. Xi . Xi
n
i=1 i=1
1n n
. (Xi . Xi2
n
i=1 i=1
60. Cramer-Rao inequality gives

Upper bound to the variance of an unbiased estimate of


Lower bound to the variance of an unbiased estimate of


Lower bound to the mean of an unbiased estimate of


None of the above


61. The method of moments for estimating the parameters was discovered and studied by

R.A. Fisher J. Neyman


Laplace Karl Pearson


62. A random sample x1, x2 ........ xn is taken from a normal population with mean zero and variance s2 then M.V.U. Estimator of s2 is
1
. Xi2 . Xi2
n
1 1

Xi . Xi
n n
63. Minimum Chi-square estimators are not necessarily

efficient consistent


unbiased none


64. Bias of an estimator will be

positive negative


either positive or negative always zero


65. If the expected value of an estimator .ˆ is not equal to its parametric value it is said to be

unbiased estimator biased estimator


consistent estimator sufficient estimator


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66. Factorisation theorem for sufficiency is known as

Rao-Blackwell theorem Cramer-Rao theorem


Chapman-Robins theorem Fisher-Neyman theorem


67. If .ˆn is an unbiased estimator of . with variance sn2 and .ˆn.., sn . 0as n .8 then estimator .ˆn is said to be

efficient sufficient


consistent none


68. For a sample from a normal population s2) where s2 is known, sample mean is

unbiased and consistent estimate of µ


unbiased but not consistent estimate of µ


consistent but biased estimate of µ


not an estimate of µ


69. Let X1, X2 and X3 is a random sample of size 3 from a population with mean µ and variance s2. Then X1 X2 X3 is

unbiased estimate of µ biased estimate of µ


not an estimate of µ unbiased estimate of s2


70. The denominator in the Cramer-Rao inequality is known as

Lower bound of the variance Fisher information


Upper bound of variance None


12
71. Let x1, x2, ....., x is a random sample from a Normal population then . xi is an
nn
unbiased estimate of

µ2 µ2 1
2
µ
µ2 1 n
72. The maximum likelihood estimators are generally

consistent and invariant invariant and unbiased


unbiased and consistent unbiased and inconsistent


73. A random sample of size 5 say x is drawn from a normal population with
12345
x x x
1 2345
unknown mean µ. Then T is an
5

unbiased estimate of µ 5 unbiased estimate of µ


biased estimate of µ unbiased estimate of


µ
5
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74. Rao-Blackwell theorem enable us to obtain minimum variance unbiased estimators through

sufficient statistics efficient statistics


consistent statistics none


75. For random sampling from normal population the maximum likelihood estimator for s2 when µ is known is
1 n 1n
. (xi µ)2 . (xi µ)2
1 n
i=1 i=1
1n2 12
. . xi
n n-1

i=1
76. In sampling from a normal population the most-efficient estimator of the population mean µ is
sample mean sample median
n
mode . xi
i=1
77. The theory of testing parametric statistical hypothesis was originally set forth by

R.A. Fisher J. Neyman


A. Wald E.L. Lehman


78. In testing hypothesis, power of a test is related to

type I error type II error


type I and II errors both none of these


79. The level of significance may be defined as the probability of

type I error type II error


no error critical region


80. The degrees of freedom in a test is related to

No. of observation in a set


Hypothesis under test


No. of independent observations in a set


None of these


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81. The ordinary run test is used for

test for randomness test for location


test for scale test for association


82. Neyman-Pearson lemma provides

a consistent test a most-powerful test


minimax test Bayes test


83. A test is said to be unbiased if

the power of the test is always greater than its size a


the power of the test is always less than its size a


power of the test is equal to its size a


none of these


84. To test H0 µ µ0 Vs H1 µ µ0 when the population S.D. is known, the appropriate test is

t-test Z-test


Chi-square test none of these


85. In the test of hypothesis H0 µ µ0 Vs H1 µ µ0 is said to be

one sided left tailed test one sided right tailed test


two sided test none of these


86. Paired t-test is applicable when the observations in the two samples are

paired correlated


equal in numbers all of these


87. The degrees of freedom for paired t-test based on n pairs of observations is

2(n n 1


2n 1 n 2


88. Degrees of freedom for .2-test in case of × contingency table is


89. Equality of several normal population means can be tested by

.2-test t-test


Normal test F-test


90. In design of experiments for analysis of variance we use

F-test .2-test


Z-test t-test


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91. The value of statistics F will be

positive negative


may be positive or negative none of these


92. Relative efficiency in Non-parametric tests is the ratio of

size of two tests power of two tests


size of samples all of these


93. The concept of asymptotic relative efficiency was given by

E.J.G. Pitman A.M. Mood


F. Wilcoxon None of these


94. Kolmogorov-Smirnov test is based on the theorem given by

N.V. Smirnov A.N. Kolmogorov


Kolmogorov-Smirnov Glivenko-Cantelli


95. Kolmogorov-Smirnov test is a

left sided test right sided test


two sided test all of these


96. The distribution of non-parametric sign test is

binomial Poisson


normal none of these


97. For non-parametric sign-test we consider the difference of observed values from the median values in terms of

magnitude only sign's only


sign and magnitude both none of these


98. The non-parametric analogous to parametric F-test is

Wilcoxon-Mann-Whitney test Wald-Wolfowitz test


Kolmogorov-Smirnov test Mood test


99. An alternative to the paired t-test in non-parametrics is

Mood test Kolmogorov-Smirnov test


Wilcoxon-Signed rank test Sukhatme test


100. The number of possible sample of size n out of N population without replacement is

Nen n


n2



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ROUGH WORK

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