LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

YB 25

FIFTH SEMESTER – April 2009

ST 5501 – TESTING OF HYPOTHESIS

 

 

 

Date & Time: 17/04/2009 / 9:00 – 12:00       Dept. No.                                                       Max. : 100 Marks

 

 

SECTION – A

 

Answer ALL questions.                                                                              10 X 2 = 20

 

1. Define Best Critical Region.
2. What is power of a test?
3. Define Monotone Likelihood Ratio property.
4. Define a UMP level α test.
5. Describe the stopping rule in SPRT.
6. State any two properties of likelihood ratio tests.
7. Write the 95 % confidence interval for population proportion based on a random sample of size n. (n > 30)
8. Describe the assumptions of t – test for testing equality of means of two independent
9. State any two assumptions of non-parametric tests.
10. Describe a test based on F- distribution.

 

 

 SECTION – B

Answer Any FIVE questions.                                                                                       5 X 8 = 40

 

11. Let X have a Poisson distribution with λ {2, 4 }. To test the null

hypothesis H₀: λ = 2 against the alternative simple hypothesis H₁: λ = 4, let the

critical region be {X₁  X₁ ≤ 3}, where X₁ is the random sample of size one. Find

the power of the test.

 

12. Based on a random sample of size n (n   30), construct a 95 % confidence interval for the population mean.

 

13. If  is a random sample from B (1, ),   (,1 ) , derive the

uniformly most powerful test for testing H₀:  =  against H₁:  >

 

14. Let be a random sample from Binomial distribution with parameter. Show that the distribution has a monotone likelihood ratio in the statistic Y =

 

15. Describe the procedure of Sequential Probability Ratio Test.

 

16. Based on a random sample of size n from B(, 0 <  , derive the SPRT

for testing H₀:  against the alternative  hypothesis H₁:  at level =0.05.

 

17. Differentiate parametric and Non-Parametric testing procedures.

 

18. Explain Kolmogorov- Smirnov one sample test.

 

SECTION – C

 

Answer any TWO questions.                                                                    2 X 20 = 40

 

19. a. State and prove Neyman-Pearson theorem.       [10]

                                                                                                                             

1. Based on a random sample of size n from a distribution with pdf

f(x, ) =        0 < x < 1

• otherwise

find the best critical region for testing null hypothesis H₀: = 2 against the

alternative simple hypothesis H₁:  = 3.                                                         [10]

 

20. Based on a random sample of size n from U(0,θ), derive the likelihood ratio test

for testing  H₀:  against the alternative hypothesis H₁:  .

 

21. a. Describe the procedure of testing H_{0 :} based on a random sample of

size n, using Wilcoxon’s statistic.                                                                    [10]

1. In SPRT, under standard notations prove that and

 

22. Explain: i) Sign test for location                          ii) Level of significance

 

iii) Test of equality of two variances      iv) Randomized test.      [ 4 x 5 ]

 

 

 

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