LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034B.Sc. DEGREE EXAMINATION – STATISTICSFIFTH SEMESTER – APRIL 2012ST 5505/ST 5501 – TESTING OF HYPOTHESES

Date : 27-04-2012 Dept. No. Max. : 100 Marks Time : 9:00 – 12:00

PART – A

Answer ALL questions: (10×2=20 Marks)

1. Distinguish between simple and composite hypothesis.2. What is meant by testing of hypothesis? 3. Define randomized test.4. Explain the meaning of level of significance. What does 5% level of significance imply?5. Which tests of hypothesis are called two-tailed tests? Give an example for it. 6. State the Likelihood Ratio Criterion.7. Write down the steps involved in a test of significance procedure for large samples.8. Define non-randomized test.9. Which types of tests are called non-parametric tests?10. Mention any two advantages of non-parametric tests.

PART – B

Answer any FIVE questions: (5×8=40 Marks)

11. Let be the probability that a coin will fall head in a single toss in order to test against . The coin is tossed 5 times and is rejected if more than 3 heads are obtained. Find the probability of Type I error and power of the test. 12. Let be a random sample from , where is known. Find a UMP test for testing against .13. Derive the likelihood ratio test for the mean of a normal population when is known.14. Derive the likelihood ratio test for the variance of a normal population when is known.15. Describe likelihood ratio test procedure and state its properties. 16. What is paired t test? What are its assumptions? Explain the test procedure.17. Explain the test procedure for testing the randomness of a sample. 18. Discuss the procedure for median tests.PART – C

Answer any TWO questions: (2×20=40 Marks)

19. (a) State and prove Neymann-Pearson Lemma. (b) Illustrate that UMP test does not exist always.20. (a) What are the applications of chi-square distribution in testing of hypothesis. (b) Explain the test procedure for testing equality of variances of two normal populations. 21. (a) What are the applications of t-distribution in testing of hypothesis? (b) Explain Wald-Wolfowitz Run test for two samples.22. (a) Explain the Chi-square test of independence of attributes in contingency table. (b) Explain the sign test for one sample.

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