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
Answer ALL questions: (10×2=20 Marks)
- 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.
PART – B
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
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.