LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
FIFTH SEMESTER – NOVEMBER 2010
ST 5505/ST 5501 – TESTING OF HYPOTHESES
Date : 01-11-10 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION – A
ANSWER ALL QUESTIONS. (10 X 2 =20 marks)
- What is a composite hypothesis? Give an example.
- Define: Critical region.
- Given an example of a density function which is not a member of the one parameter exponential family.
- When do you say a given family of density functions has MLR property?
- What are Type I and II errors?
- Define: Likelihood ratio.
- What are confidence intervals?
- State the test statistic for testing the equality of variances of two normal populations.
- Define: Empirical Distribution Function.
- Mention the use of Kolmogrov one sample test.
SECTION – B
ANSWER ANY FIVE QUESTIONS (5 X 8 =40 marks)
- A sample of size one is drawn from a population with probability density function . To test the hypothesis against the following test is suggested: “Reject H if x > 4”. Compute the size and power of the test.
- Obtain the Best Critical Region for testing H: q = q1 versus K: q = q2 ( > q1) when a sample of size ‘n’ is drawn from f(x; q ) = , 0 < x < 1 ( q > 0)
- Show that the family of Binomial densities has MLR property.
- Explain SPRT in detail.
- Derive the likelihood ratio test for testing against based on a sample of size 10 drawn from
- Explain the process of testing the significance of correlation coefficient.
- Obtain the confidence interval for the mean of a normal distribution with unknown variance.
- Explain in detail Median test.
SECTION – C
ANSWER ANY TWO QUESTIONS (2 X 20 = 40 marks)
- a) State and prove Neyman Pearson lemma.
- b) Derive the MPT of level 0.05 for testing against based on a sample
of size two drawn from
- a) Show that the family of Uniform distributions has MLR property.
- b) Derive the UMPT of level 0.05 for testing against based on a sample of size 10
- a) Obtain the SPRT for testing H: p =1/2 versus K: p = 1/3 when a sample is drawn sequentially
from B(1,p) with α = β = 0.1.
- b) Explain the procedure for testing the equality of means of two independent normal populations
with common unknown variance.
- a) Explain Mann-Whitney U test.
- b) Write a descriptive note on non-parametric methods.