Environmental Statistics Question Paper

Environmental Statistics

Course:Bachelor Of Environmental Studies

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FISRT SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ENVIRONMENTAL SCIENCE

ENS 231: ENVIRONMENTAL STATISTICS

DATE: Monday 21st December, 2009
TIME: 2.00 p.m – 4.00 p.m

INSTRUCTIONS
Answer question ONE and select any other THREE.

QUESTION ONE
a)
In a briefly, distinguish between the following pair of statistical terms. [14 marks]

i)
Expected value and expected utility

ii)
Fair bet and house edge
iii)
Dependent an independent variables
iv)
Sample and population
v)
Sample bias and sample error
vi)
Null hypothesis and alternative hypothesis
vii)
Correlation and causation
b)
Your friend is short-sighted and he is considering laser surgery to correct his
vision. You do some research and find out that the chance of a complete
correction is 39% the chance of a partial correction is 36% and the chance of no
change in vision is 7% and the chance of a worsening of his vision is 2%. Your
friend assigns a utility of +5 for achieving a complete correction, + 2 for a partial
correction, 0 for no change in vision, and – 10 for probable deterioration in vision.
He further assigns a utility of -2 to the cost and physical discomfort of the
operation. If your friend wishes to maximize his utility, do you advise him to
undergo the operation of not?

[7 marks]
Page 1 of 5

c)
A fallacy is a mistake in reasoning. The following two examples each contain
some reasoning about probabilities. Read each statement carefully and state if
you think it is a fallacy or correct. Briefly, justify your answer.

i)
Ina casino, the chance of the Mark Six (winning) numbers being exactly

the same two days in a row is extremely small. So to maximize my

chances of winning today, I should not choose yesterday’s winning
numbers.

[
3
marks]
ii)
Suppose I am in town bus terminus waiting for the matatu number 45 to
leave for Kenyatta University. The number 45 leaves from here every 25
minutes. So the longer I wait for the bus, the higher the probability that it
will leave in the next minute.

[25 marks]

QUESTION TWO

a)
Define the following two terms as used in game theory and explain their

relevance in understanding the value of an institution in enforcing laws to
contain
crime.

i)
Prisoner’s dilemma

[3 marks]

ii)
Free- rider

[3 marks]
b)
For example, imagine you are attending a school with a law enforcement.

In such a school, there is always a risk that your neighbor will break in
when you are out and steal your possessions. If he does so, you would be

better off if you went out and stole his things. In fact, even if he doesn’t

steal things, you are still better off if you steal his things. In utility terms

the worst outcome (-5) in having your things stolen without stealing

anything back. If you steal some stuff back, the outcome isn’t so bad (-3).

If neither of you steals anything, the outcome is neutral (0) and if you
steal things but nothing is stolen from you, you get an overall benefit(+2).

[15
marks]

Page 2 of 5

i)
Create a utility table corresponding to the information provided
above.

[5
marks]
ii)
If you always act in self – interest, are you better of stealing or not

stealing in a school without law enforcement?
[4 marks]

QUESTION THREE
a)
Using two specific examples, explain when it might be more accurate to
summarize your dataset using the median rather than mean.
[ 6 marks]
b)
The following table shows students’ marks for a particular coursework
assignment( the figures are invented)
Student number
Mark
00001 59
00002 61
00003 57
00004 0
00005 51
00006 64
00007 70
00008 0
00009 55
00010 0

i)
Calculate the mean and median values for this data. Why are they so different?
[5 marks]
ii)
Suppose there is a university policy that the mean mark for each assignment must

be close to 60. In view of the mean you have calculated above, what would a

professor do to comply the policy?

[2 marks]
iii)
In your view, does it seem like the right response in this particular instance?

Comment, in a sentence or two.

[2 marks]

Page 3 of 5

QUESTION FOUR
a)
What is the difference between standard deviation and interquartile range as

two methods of measuring spread in a set of data?

[3 marks]

b)
The following table represents annual trends in financial allocations from

Treasury for primary schools in the past decade.

Allocation
Year
Allocation ( in Millions)
1999 50

2000 20
2001 30
2002 70
2003 100
2004 150
2005 60
2006 85
2007 200
2008 125
2009 130

i)
Calculate the mean and the standard
deviation.
[4
marks]
ii)
How many standard deviations below the mean is the 2000 figure? How many

standard deviations above the mean is the 2008 figure?

[4 marks]
iii)
Find the median and the interquartile
range.
[
4
marks]

QUESTION FIVE
a)
Identify possible sources of bias in each of the following examples:

i)
CITIZEN TV invites viewers to call in and participate in a poll on some

item of current interest.

[ 2 marks]
Page 4 of 5

ii)
STEADMAN conducts a political poll by calling numbers picket at
random
from
a
cell
phone
directory.
[2
marks]
iii)
Tests to determine the incidents of HIV/ AIDs in the population are

conducted on a random sample of women attending prenatal clinics across
the
country.
[
2
marks]
b)
Your local MP hires you estimate his support in the forthcoming election. A poll
of 1000 people indicates that he has the support of 52% of people, with a margin
of error of 3 percentage points. Your MP would like a more accurate estimate,
however. How many people would you need poll in order to reduce the margin
of error to 1 percentage point?

[5 marks]
c)
What does your answer in (b) above teach you about the practicalities of reducing
the margin of error beyond a certain threshold ?

[4 marks]
Page 5 of 5

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