Introduction to Mathematical Statistics (MATS3206)
Mathematics and Computer Science - MCS
Semester: Second Semester
Level: 300
Year: 2018
UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE
SECOND SEMESTER EXAMINATION 2017/2018 SESSION
COURSE CODE: Mats 3206
CREDIT LOAD: 6 CREDITS
INSTRUCTIONS: ANSWER ALL QUESTIONS
DURATION: 2 HOURS
1. A certain population consist of the digit 2, 6, 9, 15.
a) Find the mean, u and the variance, a
2
, of the population.
b) Draw up a frequency distribution of the mean of all possible samples of size 2 that
can be taken without replacement from the population.
c) Find the mean and variance of the sampling distribution of means.
2. (a). A random sample from a Bin (n,p) distribution yields the following values
4,2,7,4,1,4,5,4. Find method of moments estimates of n and p using
and S
2
.
(b). given the probability density function of a poisson distribution and six observed
values 4,10,4,8,7,7. Find the maximum likelihood estimate of the poission mean
3. Let x
1
, x
2
, x
3
. . , x
n
be a random sample of size n from a poisson distribution with
unknown parameter
.
If the sample size is 10 and we are to test H
o
:
=30 against Hi
=36 at 5% level of significance. Determine the value of a positive constant K such
that,
(;)
(,)
≤
4. (a) To test Ho:=50 against H1: <50, a random sample of size n=24 is obtained
from a population that is known to be normally distributed with mean 47.1 and
standard deviation 12. Test at the 5% level of significance whether the null
hypothesis, H
o
could be rejected, using the P-Value method.
(b) a random variable, X is normally distributed with mean , u and variance 4. A sample
of size n=12 has mean 13. Find a 95% confidence interval for the population mean .
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5. (a) The daily demand for loaves of bread at exclusive supermarket is given in the
following table.
Days of
week
Mon
Tues
Wed
Thurs
Fri
Sat
Number of
loaves sold
110
150
330
280
430
500
Test at =0.01 that the number of loaves of bread sold does not depend on the day of the
week. (Hint: use chi-square test of Goodness of Fit).
(b) An experiment was conducted to find out the number of hours that university students
spend watching television per week. It was discovered that for a sample of 10 students,
the following times were spent watching television:
8,4,7,5,9,7,6,9,5,7,
Calculate the mean and variance of the sample
Construct a 95% confidence interval for
END
Course instructor
NTAM YUH TERENCE.
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