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Statistics For Economist 1 Question Paper

Statistics For Economist 1

Course:Bachelor Of Economics

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ARTS AND BACHELOR OF ECONOMICS

EES 202:
STATISTICS FOR ECONOMIST 1

=================================================================
DATE:
MONDAY 28TH DECEMBER 2009
TIME: 2.00 P.M. – 4.00 P.M.

INSTRUCTIONS

Answer Question 1 and any other two.

Question 1

a)
The price – earning ratio for 30 different stocks on the New York stock exchange are

as shown here.
4.8 5.2 7.6 5.7 6.2 6.6 7.5 8.0 9.0 7.7
3.7 7.3 6.7 7.7 8.2 9.2. 8.3 7.3 8.2 6.5
5.4 9.3 10.0 7.3 8.2 9.7 8.4 4.7 7.4 8.3

i)
According to Chebshev’s Theorem, at least how many price – earnings ratios
lies within two standard deviations of the mean?(3 marks)

ii)
How many actually do lie within two standard deviations of the mean?(3 marks)

Page 1 of 5
b)
In 500 small scale industrial projects in the Jua Kali sector, the profit on
investment ranged from 0 to 30%, no unit sustaining loss. The median rate of
profit was 15% and upper quartile was 20%. The rate of profit distribution is a
follows:

% rate of profit 0-5 5-10
10-15
15-20
20-25
25-30

No of Units
25
75
X
Y
Z
50

Required

i)
The valuesX,Y,and Z(6marks)

ii)
The mode of the distribution, Interpret its meaning.(3 marks)

iii)
The proportion of the industrial units whose rate of profit does not exceed the
modal value calculated in part (ii) above.(4 marks)

c)
Students taking the graduate Management Aptitude Test averaged 812 with a

standard deviation of 145. Only those in the top 20 percent can apply for a particular

scholarship. Baraka Opoma received a 900 on the test. Can he apply?
(4 marks)
d)
With illustrations distinguish between Conditional and dependent probability.(4 marks)
e)
Distinguish between continuous and discrete distributions.(3marks)

Question 2
a)
Identify the characteristics of a good measure of central tendency.
(4 marks)
b)
A check of voter registration records in one precinct Peoria County, Illinois reveals

that there are 512 registered voters. Of those, 309 are democrats and 150 are

Republicans. The rest are registered independent or as a third party. Of the 512

voters, 323 are men and 189 are women. Two registered voters must be selected at

random to serve as pool watchers. The county registrar must determine the

composition of these poll watches in hopes of ensuring equal representation by sex
Page 2 of 5

and party affiliation. Using the subscripts 1 and 2 to indicate the first and second
selection, respectively, the registrar wishes to know the probability that:

a)
Both are Democrats; P (D1 and D2)(2marks)

b)
Both are republicans; P(R1 and R2)
(2
marks)

c)
The first is a Democrat and the second is a Republican; P(D1 and R2).(3marks)

d)
The first is Republican and the second is a Democrat;P(R1 and D2)(3 marks)

e)
Both are Women; P(W1 and W2).(2marks)

f)
Both are men; P (M1 and M2)(2 marks)

g)
One is a man one is a woman.(2 marks)

NB: Since two people are to be selected to serve as poll watches, it is
impossible to replace the first before the second is chosen. Drawings
must be done without replacement.

Question 3
a)
Distinguish between the following terms using relevant illustrations:

a.
Components and multiple bar charts.(2 marks)
b.
Frequency and Probability tables.(2marks)
c.
Geometric and arithmetic mean(2marks)
d.
Binomial and Poisson distribution.(2marks)
e.
Coefficient of variation and variance(2marks)
b)
Three firms producing microchips in south C, Nairobi, report the following values for

the number of employees, average daily output, and standard deviation in daily output

over the past 100 days.

Firm Employees Output Standard deviations
1 95 110 27
2 63 253 32
3 87 312 134

i)
Which firm seems to be most consistent in its level of output? Explain.
(2 marks)

ii)
Assuming the data for all three firms are normally distributed, use empirical

Rule to determine the range of output for each firm on approximately 68 of
the 100 days and 95 of the 100 days.(6 marks)

iii)
Which firm had the highest average level of output per employee? What was
that average?(2 marks)

Question 4
a)
Identify and briefly explain the functions of statistics.(7 1/2 marks)
b)
The observations listed are times (in minutes) that 30 students took to complete their

first statistics test.

42.3 70.0 37.2 69.2 41.9 39.2 67.7 52.6 63.2 39.2
58.9 45.5 53.3 61.9 45.7 42.7 69.1 55.5 63.9 41.7
38.9 52.4 68.3 61.2 70.1 39.2 68.3 52.5 64.9 69.8

Required:

i)
Simplify the data in form of frequency table (7 classes).(6 marks)

ii)
Construct more than cumulative frequency curve and estimate
50th percentile.(6 ½ marks)

Question 5
a)
Tossing an unbiased coin fits the requirements for binomial distribution. Give
reasons to justify.(4marks)
b)
Given that an experiment of rolling a six sided die yield a probability distribution,
compute the expected value and variance of the experiment.(6 marks)
c)
By giving necessary illustrations, briefly explain the stages to statistical investigation.
(10 marks)

Statistics For Economist 1 Question Paper

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