LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2010

ST 5505/ST 5501 – TESTING OF HYPOTHESES

 

 

 

Date : 01-11-10                     Dept. No.                                                     Max. : 100 Marks

Time : 9:00 – 12:00

SECTION – A

 

 

ANSWER ALL QUESTIONS.                                                                                        (10 X 2 =20 marks)

 

1. What is a composite hypothesis? Give an example.
2. Define: Critical region.
3. Given an example of a density function which is not a member of the one parameter exponential family.
4. When do you say a given family of density functions has MLR property?
5. What are Type I and II errors?
6. Define: Likelihood ratio.
7. What are confidence intervals?
8. State the test statistic for testing the equality of variances of two normal populations.
9. Define: Empirical Distribution Function.
10. Mention the use of Kolmogrov one sample test.

 

SECTION – B

 

ANSWER ANY FIVE QUESTIONS                                                                               (5 X 8 =40 marks)

 

11. A sample of size one is drawn from a population with probability density function . To test the hypothesis against the following test is suggested: “Reject H if x > 4”. Compute the size and power of the test.
12. Obtain the Best Critical Region for testing H: q = q₁ versus K: q = q₂ ( > q­₁) when a sample of size ‘n’ is drawn from f(x; q ) = , 0 < x < 1 ( q > 0)
13. Show that the family of Binomial densities has MLR property.
14. Explain SPRT in detail.
15. Derive the likelihood ratio test for testing against based on a sample of size 10 drawn from
16. Explain the process of testing the significance of correlation coefficient.
17. Obtain the confidence interval for the mean of a normal distribution with unknown variance.
18. Explain in detail Median test.

(P.T.O)

SECTION – C

 

ANSWER ANY TWO QUESTIONS                                                                     (2 X 20 = 40 marks)

 

19. a) State and prove Neyman Pearson lemma.
20. b) Derive the MPT of level 0.05 for testing against based on a sample

of size two drawn from

20. a) Show that the family of Uniform distributions  has MLR property.

 

1. b) Derive the UMPT of level 0.05 for testing against based on a sample of size 10

drawn from

 

21. a) Obtain the SPRT for testing H: p =1/2 versus K: p = 1/3 when a sample is drawn sequentially

from B(1,p) with α = β = 0.1.

1. b) Explain the procedure for testing the equality of means of two independent normal populations

with common unknown variance.

 

22. a) Explain Mann-Whitney U test.
23. b) Write a descriptive note on non-parametric methods.

 

 

 

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