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Exam Details

2020 Statistics Paper - II

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Questions 80
Duration 180 mins
Package National Defence Academy and Naval Academy Examination (I) & (II) - Previous Year Papers

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Difficulty distribution

Hard 27 33.8%
Easy 27 33.8%
Medium 26 32.5%

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Multiple Choices 80 100%

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Sample questions from this paper

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1
2020 · Unclassified
2020 Statistics Paper - II
Suppose the probability mass function of a random variable X under the parameter = 0 and = 1, 1 0 0 is given by | X | 0 | 1 | 2 | 3 | | p0(x) | 0 | 0 | 00 | 05 | | p1(x) | 0 | 0 | 00 | 00 | Define a test function 8 such that 8(x) = {1, if x = 0, 1 0, if x = 2, 3 For testing H0 : = 0 against H1 : = 1 the test 8 is
A
a most powerful test at level 005
B
a biased test
C
test with power 0 0
D
test of size 0 1
2
2020 · Unclassified
2020 Statistics Paper - II
Consider the distribution having probability density function of a random variable X as f(x, ) = {1/, 0 x 0, elsewhere Let 1 X 15 be the critical region to test the hypothesis H0 : = 15 against H1 : = 2. Then
A
size of the test is 0 and test is unbiased
B
size of the test is 1/2 and test is unbiased
C
size of the test is 1/3 and test is biased
D
size of the test is 1/3 and test is unbiased
3
2020 · Unclassified
2020 Statistics Paper - II
Let X be a random variable with pmf under H0 and H1 given by | X | 1 | 2 | 3 | 4 | 5 | 6 | | p0(x) | 0 1 | 0 1 | 0 1 | 0 1 | 0 1 | 0 5 | | p1(x) | 0 5 | 0 4 | 0 3 | 0 2 | 0 1 | 05 | Consider a test function 8(x) as 8(x) = {1, if X = 1, 2 05, if X = 3 0, otherwise Then which one of the following is correct ?
A
8(x) is a most powerful test of level = 0 3
B
8(x) is a most powerful test of level = 0 3 with power 0 975
C
8(x) has size 025 and power 0 975 but it is not a most powerful test with level = 0 3
D
8(x) is not a most powerful test of level = 025
4
2020 · Unclassified
2020 Statistics Paper - II
Which one of the following parameters is correct in case of Likelihood Ratio Test (LRT) ?
A
In LRT, control is not affected over the probabilities of type-I error by suitably choosing the cut-off point 0
B
LRT always gives unbiased test
C
When null hypothesis is composite, the LR critical region will be always similar
D
Under certain assumptions, an LRT will be consistent
5
2020 · Unclassified
2020 Statistics Paper - II
An estimator to be a good estimator,
A
should be efficient but not necessarily unbiased
B
should be consistent but not necessarily efficient
C
should be unbiased but not necessarily sufficient
D
should be unbiased, consistent, sufficient and efficient
6
2020 · Unclassified
2020 Statistics Paper - II
For Cauchy distribution, consider the following statements : 1. Sample mean is consistent estimator of the population median. 2. Sample median is consistent estimator of the population median. Which of the above statements is/are correct ?
A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2