Introduction to Statistical Methods (MATS2206)
Mathematics and Computer Science - MCS
Semester: Resit
Level: 200
Year: 2018
REPUBLIC OF
The UNIVERSITY OF
CAMEROON
BAMENDA
P.O BOX 39 Bambili
School/
Faculty: Science_
Department:
MATHS/COMP SCIENCE
Lecturer(s): Dr. KUM CLETUS
KWA
Course Code: MAT2108
Course Title: INTRODUCTION TO
STATISTICAL METHODS
Date: 11/O9/2018
Hall:
Time: 2 HOURS
1. Consider the following sample data: 12. 14,10, 14, 18, 11, 21, 24, 20,16, 22, 16.
Find the mean, median and the standard deviation for the data. (10 marks)
2. (a) Let X
1
, X
2
, … ,
X
n
be a random sample from a Poisson distribution which has as pdf
f(x) =
Find the maximum likelihood estimator for the parameter . (10 marks)
b) Let X
1
, X
2
, … ,
X
n
denote a random sample from the probability density function
f(x: )
(10 marks)
Find an estimator for
by the method of moments.
3. A study has been made to compare the nicotine contents of two brands of cigarettes. Ten cigarettes of
Brand A had an average nicotine content of 3.1 milligrams with a standard deviation of 0.5 milligram,
while eight cigarettes of Brand B had an average nicotine content of 2.7 milligrams with a standard
deviation of 0.7 milligram. Assuming that the two sets of data are independent random samples from
normal populations with equal variances, construct a 95% confidence interval for the difference between
the mean nicotine contents of the two brands of cigarettes. (10 marks)
4. A single observation of a random variable having an exponential distribution f(x,
)=
is used
to test H
0
:
= 2 versus H
1
:
=
4. If the null hypothesis is accepted if and only if the random variable is
less than 4, find and . (12 marks)
5. Suppose that X
1
, X
2
, … ,
X
n
constitute a random sample from a normal distribution with unknown mean
and known variance !
2
. We wish to test H
0
: " = "
o
against H
1
: " = "
1
, where "
1
> "
o
a) Using the Neyman - Pearson lemma, find the best critical region for the test with significance level .
b) Find the critical value k of the test statistic. (18 marks)
Dr. Kum Cletus Kwa: September 2018
www.schoolfaqs.net
