Question 1:
a) State the prove Lehmann-Pearson Lemma. Give its significance in testing of hypothesis.
b) Construct a LR test to test Ho: µ = µo against H1: µ ≠ µo in sampling from N (µ, σ2), where both µ and σ2 are unknown.
Question 2:
a) Explain Kolomogolor-Sminnor one sample and two sample tests.
b) Describe the term Mann-Whitney U-test.
Question 3:
a) Show that SPRT terminates finally with certainty.
b) Define the term OC and ASN functions of SPRT. Derive them for testing the proportion of a binomial distribution.
Question 4:
a) State and prove the Wald’s fundamental identify.
b) Explain the Wald’s SPRT. Derive OC and ASN functions for testing the mean of a normal distribution with unit variance.
Question 5: Write brief notes on any two of the given:
a) Factorization theorem.
b) CAN estimators.
c) Monotone likelihood ratio and UMP tests.
d) Median test.
e) SPRT for testing Poisson parameter.