THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT 1302 PROBABILITY AND STATISTICS II
(200910)
EXAMPLE CLASS 9
1. The numbers of members of a learned society born in the different months are as
sumed to be Poisson random variables with probably different means. The numbers
are observed as follows:
J
F
M
A
M
J
J
A
S
O
N
D
39
28
51
49
48
48
41
39
33
60
48
44
It is claimed that members are born at a constant rate throughout the whole year.
Test
H
0
: a constant rate against
H
1
: the rate may vary from month to month.
(a) Determine the likelihood ratio for the specified hypotheses.
(b) Calculate the (approximate) pvalue of the generalized likelihood ratio test
with the help of Wilk’s Theorem.
2. From each of six batches of seed a random sample of 100 seeds was selected for
sowing.
The numbers of seeds that failed to germinate in the six samples of 100
seeds were 12, 20, 9, 17, 24, 16. Calculate the pvalue for the Pearson chisquared
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 SMSLee
 Statistics, Probability, Pearson's chisquare test, Likelihoodratio test, likelihood ratio, UNIVERSITY OF HONG KONG DEPARTMENT, xi ln xi, xi ln

Click to edit the document details