Total No. of Questions 10] [Total No. of Pages 02
M.Sc. DEGREE EXAMINATION, MAY 2018
First Year
STATISTICS
Statistical Inference
Time 3 Hours Maximum Marks :70
Answer any five questions.
All questions carry equal marks.
Q1) Explain the terms sufficiency ii) unbiasedness with examples.
State and prove factorization theorem.
Q2) State and prove Blackwell theorem.
Let x1, x2 ….. xn be a random sample from the distribution with p.d.f.
if α x β where θ and 0 β <α. Obtain Mvu
estimators of
2
α
and β −α .
Q3) What is interval estimation? Explain with an example.
Describe the maximum likelyhood method of estimation. Find an ML
estimator for θ in f 1)x x 1. θ θ θ
Q4) Obtain confidence limits for the parameter in with confidence coefficient
(1−α
Explain the method of moments in brief.
Q5) State and prove Naymann pearson lemma.
Explain the concept of monotone likelyhood Ratio in brief.
Q6) What is the difference between randomized and non-randomised tests?
Explain in brief.
Consider n Bernoulli trials with probability of success p for each trial. Derive
the likelyhood ratio test for H0 P=P0 against H1:P>P0 and H1: P<P0. Then
show that they are identical with UMP tests.
Q7) Explain the procedure of Mann-whitney test in brief.
What are the applications of Wilcoxon test? Explain its procedure.
Q8) Is there a difference between health services workers and education service
workers in the amount of compensation of employers pay them per hour
suppose a random sample of seven health service workers is taken along with
a random sample of eight education service workers from different parts of
the country. Each of their employers is interviewed and figures are obtained
on the amount paid per hour for compensation per hour. Use Mann-Whitney
test to determine whether these two populations are different in employee
compensation.
Health service
worker
26.19 19.80 22.36 18.75 21.90 22.96 20.75
Education
service worker
20.10 23.88 25.50 21.64 24.85 25.30 24.12 23.45
Explain how median test is differentiate in testing two means? Also write the
procedure of median test.
Q9) Describe SPRT procedure in brief.
Define OC and ASN functions of the SPRT.
Q10)a) Derive SPR test to test the parameter λ of a Poisson Distribution obtain its
OC and ASN functions.
Describe SPRT in the case of normal distribution.