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Business Statistics Question Paper

Business Statistics

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
INSTITUTE OF OPEN LEARNING
UNIVERSITY EXAMINATIONS 2008/2009
EXAMINATION FOR THE DEGREE OF BACHELOR OF COMMERCE
BMS 200: BUSINESS STATISTICS

DATE: MONDAY, 5TH JANUARY 2009
TIME: 11.00 A.M. – 1.00 P.M.

INSTRUCTIONS:
? Answer question ONE and any other TWO questions.
? Show ALL your workings.

QUESTION ONE

(a)
Differentiate between the following terms as used in statistics:

i)
Descriptive Statistics and Inferential Statistics

(2 marks)

ii)
Skewness and Kurtosis

(2 marks)

(b)
Briefly explain the importance of time series analysis to a business organization.

(6 marks)

(c)
At Nakumatt Supermarket, 60% of the customers pay by credit card. Find
the probability that in a randomly selected sample of ten customers:

i)
Exactly two pay by credit card

(2 marks)

ii)
More than seven pay by credit card

(2 marks)

(d)
On average the school photocopier breaks down eight times during the
school week (Monday to Friday). Assuming that the number of breakdowns
can be modeled by a Poisson distribution, find the probability that it breaks down:
i)
Five times in a given week

(2 marks)
ii)
Once on a Monday

(2 marks)
iii)
Eight times in a fortnight

(2 marks)

2

(e)
The following marks belong to 99 students of a secondary school in
Keroka Municipality.
Marks
Number of students
0 – 10
10
10 – 20
?
20 – 30
25
30 – 40
30
40 – 50
?
50 – 60
10

On later analysis, it was discovered that two class interval frequencies were missing.
The median score was found to be 30.
Required:
i)
Find the missing frequencies

(3 marks)
ii)
Find the mean mark

(2 marks)

iii)
Determine the modal mark of the students

(2 marks)

iv)
Find the standard deviation

(3 marks)

QUESTION TWO

a)
Describe the four components of time series analysis.

(6 marks)
(b)
Briefly explain four factors that must be taken into consideration when
constructing index numbers.

(6 marks)
(c)
A firm’s marketing manager believes that total sales for the firm next year
can be modeled by using a normal distribution with a mean of KSh.2.5 million
and a standard deviation of KSh.300,000.
i)
What is the probability that the firm’s sales will exceed KSh.3 million?
(2 marks)
ii)
What is the probability that the firm’s sales will fall within
KSh.150,000 of the expected level of sales?

(2 marks)
iii)
In order to cover fixed costs, the firm’s sales must exceed the
break-even level of KSh.1.8 million. What is the probability that
sales will exceed the break-even level?

(2 marks)

3

iv)
Determine the sales level that has only a 9% chance of being
exceeded next year.

(2 marks)

QUESTION THREE

a)
Using relevant examples, describe the four levels of measurement used in statistics.

(6 marks)
b)
Students in the BMS 200 class were polled by a researcher attempting to
establish a relationship between hours of study in the week immediately
preceding the end of semester exam and the marks received on the exam.
The surveyor gathered the data listed in the accompanying table.
Hours of study
Exam score
25
93
12
57
18
55
26
90
19
82
20
95
23
95
15
80
22
85
8
61

i)
Find the least squares regression line by identifying the appropriate
dependent and independent variable.

(7 marks)
ii)
Interpret the meaning of the values of the constants calculated in
part (i).

(3 marks)
iii)
Compute the coefficient of correlation and coefficient of
determination and interpret.

(4 marks)

4

QUESTION FOUR

(a)
Differentiate between the following terms as used in statistics.

i)
Type I error and Type II error

(2 marks)

ii)
Two tailed test and one tailed test

(2 marks)

(b)
Briefly explain four limitations of consumer index numbers.

(6 marks)

(c)
The following data relates to the prices and quantities of three commodities
in the years 2001 and 2005.

2001
2005
Commodity
Price
Quantity
Price
Quantity
A
65
20
135
30
B
95
8
160
5
C
150
5
320
8

From the above data, calculate the price index numbers for 2005 taking 2001 as
the base year using:
i)
Laspeyer’s index number

(2 1 marks)
2
ii)
Paasche’s index number

(2 1 marks)
2
iii)
Fisher’s ideal index number

(2 1 marks)
2
iii)
Marshall-Edgeworth index number

(2 1 marks)
2

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Business Statistics Question Paper

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