LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

**B.Sc.** DEGREE EXAMINATION – **STATISTICS**

FIFTH SEMESTER – **APRIL 2012**

# ST 5505/ST 5501 – TESTING OF HYPOTHESES

Date : 27-04-2012 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

__PART – A__

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**Answer ALL questions: (10×2=20 Marks)**

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

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__PART – B__

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

- 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.
- Let be a random sample from, where is known. Find a UMP test for testing against.
- Derive the likelihood ratio test for the mean of a normal population when is known.
- Derive the likelihood ratio test for the variance of a normal population when is known.
- Describe likelihood ratio test procedure and state its properties.
- What is paired
*t*test? What are its assumptions? Explain the test procedure. - Explain the test procedure for testing the randomness of a sample.
- Discuss the procedure for median tests.

__PART – C__

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

- (a) State and prove Neymann-Pearson Lemma.

(b) Illustrate that UMP test does not exist always.

- (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.

- (a) What are the applications of
*t*-distribution in testing of hypothesis?

(b) Explain Wald-Wolfowitz Run test for two samples.

- (a) Explain the Chi-square test of independence of attributes in contingency table.

(b) Explain the sign test for one sample.