Solapur University Question Paper,STATISTICS (Special Paper – XIII) Statistical Inference – II,B.Sc. (Part – III) (Semester – VI),2014 Question Paper

Solapur University Question Paper
B.Sc. (Part – III) (Semester – VI) Examination, 2014
STATISTICS (Special Paper – XIII)
Statistical Inference – II
Day and Date : Thursday, 10-4-2014 Max. Marks : 50
Time : 11.00 a.m. to 1.00 p.m.
Instructions : 1) All questions are compulsory and carry equal marks.
2) Figures to the right indicate full marks.
1. Choose the correct alternative : 10
i) The most pragmatic approach for determining (1− α)% confidence interval is
to find out
a) Zero width confidence interval
b) Equal tail confidence interval
c) The combined area of both the tails is equal to α
d) None of the above
ii) For a random sample of size n from a N( , )
2
μ σ with known μ, the degrees of
freedom of 2
2
2 i (x )
σ
Σ − μ χ = is
a) n – 1 b) n c) n + 1 d) 0
iii) The hypothesis under test is
a) simple hypothesis b) alternate hypothesis
c) null hypothesis d) none of the above
iv) If β is probability of type – II error and θ is true parameter, 1− β(θ) is called
a) Power of the test b) Power function
c) OC function d) None of the above
P.T.O.
Seat
No.
SLR-C – 162 -2-
v) Neyman – Pearson lemma provides
a) an unbiased test b) an admissible test
c) a most powerful test d) minimax test
vi) Testing H : 1500 0 μ = against H : 1500 1 μ < leads to the test of
a) one sided lower tailed b) one sided upper tailed
c) two-tailed d) all the above
vii) In SPRT decision about the hypothesis is taken
a) after each successive observation
b) after a fixed number of observations
c) atleast after five observations
d) when the experiment is over
viii) Most frequently used method of breaking the tie is
a) midrank method b) average statistics approach
c) to omit tied values d) most favourable statistic approach
ix) Ordinary sign test utilizes
a) Poisson distribution b) Binomial distribution
c) Normal distribution d) None of the above
x) In Wilcoxon’s sign-ranked test the statistic T+ is distributed with variance
a) n(n – 1) (2n – 1)/24 b) n(n + 1) (2n + 1)/24
c) n(2n + 1)/12 d) n(n – 1) (2n + 1)/12
2. Answer any five of the following. 10
i) Define an interval estimation.
ii) Giving an example, define a simple hypothesis and a composite hypothesis.
iii) Define a test statistic and give an example.
iv) Define likelihood ratio test (L.R.T.).
v) Giving an example, define a run in the run test.
vi) For the median test write the testing problem.
3. A) Answer any two of the following. 6
i) Based on a random sample of size n from f(x ; ) x , x 1, 1 θ = θ θ < < θ− show
that the best critical region (B.C.R.) for testing H : 1 0 θ = against H : 2 1 θ =
is ≥ =
π
i
n
x i 1 C.
ii) State the properties of (L.R.T.).
iii) Give the merits of non-parametric tests as compared to parametric tests.
B) Write a note on two sample run test. 4
4. Answer any two of the following. 10
i) Obtain 100(1− α)% confidence interval for the mean μ of N( , ), 2
μ σ when 2
σ
is known
ii) Obtain 100(1−α)% confidence interval for 2
σ when μ is known of N( , ). 2
μ σ
iii) Based on a random sample of size n from ;
x !
e p(x; )
x λ λ =
−λ
 x = 0, 1, 2, ...,
show that the most powerful critical region of size not exceeding α for testing
0 0 H : λ = λ against 1 1 H : λ = λ is of the form
0 1 x ≤ A if λ > λ α
0 1 x ≥ B if λ < λ α
5. Answer any two of the following. 10
i) Let X be a Bernoulli variate with p.m.f. p(x, ) (1 ) , x 1−x θ = θ − θ x = 0, 1 ; 0 < θ < 1.
Construct SPRT of strength (α, β) for testing 0 0 H : θ = θ against
H : ( ). 1 1 1 0 θ = θ θ > θ
ii) Obtain the (L.R.T.) for testing 0 0 H : μ = μ against 1 0 H : μ ≠ μ based on a random
sample from N( , )
2
μ σ when both μ and 2
σ are unknown.
iii) Explain in brief the median test.
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