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)

 

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)

 

1. 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.
2. Let  be a random sample from, where  is known. Find a UMP test for testing  against.
3. Derive the likelihood ratio test for the mean of a normal population when  is known.
4. Derive the likelihood ratio test for the variance of a normal population when  is known.
5. Describe likelihood ratio test procedure and state its properties.
6. What is paired t test? What are its assumptions? Explain the test procedure.
7. Explain the test procedure for testing the randomness of a sample.
8. Discuss the procedure for median tests.

PART – C

 

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

 

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

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

1. (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.

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

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

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

(b) Explain the sign test for one sample.

 

 

 

Go To Main page

Latest Govt Job & Exam Updates:

View Full List ...