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)

(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.

(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.