M.Sc. (Semester II) (CBCS) Examination Oct/Nov-2017
Statistics
THEORY OF TESTING OF HYPOTHESES
Day Date: Friday, 24-11-2017 Max. Marks: 70
Time: 10:30 AM to 01.00 PM
Instructions: Attempt five questions.
Q. No. and Q. No are compulsory.
Attempt any three from Q. No. to Q. No.
Figures to the right indicate full marks.
Q.1 Choose correct alternative: 05
Size g the test is
Always greater than or equal to the level of significance
Always less than or equal to the level of significance
Always equal to the level of significance
None of these
The family of distribution of . based on a random
sample from possesses MLR property in

None of these
For testing simple vs. simple hypotheses, most powerful test and
likelihood ratio tests are
The same Not comparable
Different None of these
A test function 0.5 for all has power.
1 0.5
0 None of these
A most powerful test is
Biased Unbiased
Either or None of these
Fill in the blanks. 05
UMP is always
UMP test leads to intervals.
The asymptotic distribution of the likelihood ratio statistic follows
Generalized NP lemma is used to construct
The degrees of freedom associated with 5X4 contingency table is
State the following sentence are True or False: 04
If is a test function, then 1 − is also a test function.
Every similar test has a Neyman-structure.
Sign test utilizes poisson distribution.
A hypothesis s known as simple, if it is not specified completely.
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SLR-MS-652
Q.2 Answer the following: 06
MLR Property
Run Test
Write short notes on the following: 08
U-statistic
Shortest length confidence interval
Q.3 State and prove existence part of Neyman-Pearson Lemma. 07
Define:
Most Powerful Test
Unbiased Test
Illustrate with an example M.P. test is unbiased.
07
Q.4 Explain the terms:
Power function
Randomized Test
Similar Test
UMP Test
07
Let … … . . be a r.s. from 1 distribution. Examine whether a
UMP test exists for testing Vs
07
Q.5 Explain the terms:
Confidence level
Pivots
UMA confidence interval
UMAU confidence interval
07
Obtain the shortest length confidence interval of confidence level
1−∝ for based on a sample of sixe from when is
unknown.
07
Q.6 Define likelihood ratio test. Derive the same for test 0 against
0 based on a r.s. of size from 1 distribution.
07
Describe goodness of fit test based on chi-square distribution. 07
Q.7 Obtain UMPU level ∝ test for testing the hypothesis against
based on
07
Obtain M.P. level ∝ test for testing 1 Vs 0 for a single
observation from 1 − 0 1
Also find power of the MP test.