Introduction to Statistical Methods (MATS2206)
Mathematics and Computer Science - MCS
Semester: Second Semester
Level: 200
Year: 2018
THE UNIVERSITY OE BAMENDA
FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS AND STATISTICS
MAGS2206 - INTRODUCTION TO STATISTICAL METHODS
CONTINUOUS ASSESSMENT: 2017/2018 Academic Year
TIME ALLOWED: 1 hour 30 minutes.
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. (7 marks)
2.
a) Suppose a sample x
1
, x
2
, … , x
n
is modelled by a Poisson distribution with parameter , so that
fx(x;) =
;
)
=
⋋
−
!
: x=0,1,2…
Find the maximum likelihood estimate for . (5 marks)
b) Let x
1
, x
2
, … , x
n
denote a random sample from the probability density function
f(x: )=
θ + 1)x
0 < x < 1
0 elsewhere
Find an estimator for 0 by the method of moments. (5 marks)
3.
Suppose we are given that a random sample x
1
, x
2
, … , x
n
size n = 36 and that 24.5 with a
sample standard devation s = 2 .
a)
Construct a 95% confidence interval for the population mean //. (4 marks)
b)
If the sample size was n = 25 with s
2
= 4. What will be the 95% confidence interval for ? (4 marks)
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