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Introduction To Business Statistics Question Paper
Introduction To Business Statistics
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2010
UNIVERSITY EXAMINATIONS: 2009/2010
FIRST YEAR STAGE 3 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 105: INTRODUCTION TO BUSINESS STATISTICS (SUNDAY)
DATE: APRIL 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and Any other TWO Questions
QUESTION ONE (30 MARKS)
a) State three methods of data collection (3 Marks)
b) The consistency of sales representatives of a company is to be determined, the monthly sales of one
of the representatives in the course of one year is given below:
46, 60, 45, 53, 50, 47, 55, 50, 48, 51, 54, 53.
Determine:
i) Mean. (2 Marks)
ii) Standard deviation. (3 Marks)
iii) Coefficient of variation and comment on the consistency. (3 Marks)
c) Find the weighted price index for the following basic goods in a two year period and comment on
the rise of the cost of living index over the period.
(5 Marks)
d) In the human resource department there are 5 male and 4 female members of staff. Two members
are chosen randomly to attend a conference. Find the probability that:
i) One is a female and the other male.
2006 2007
Item Weight Price Price
Sugar 4 80 95
Flour 5 50 58
Salt 2 8 12
Fat 3 75 84
2
ii) They are both female.
(5 Marks)
e) In an effort to compare the performance of the two branches of a Marketing firm the following
information was obtained
Branch A Branch B
No. of sales representatives 100 100
Mean sales 1200 1145
Standard deviation 80 92
Determine if the performance of the two branches is significantly different at 95% level of
confidence. (5 Marks)
f)
i) Define the term time series (1 Mark)
ii) Compute three year moving average for the following time series to 1 decimal place.
Year 2001 2002 2003 2004 2005 2006 2007 2008
Amount 430 451 444 460 469 500 490 510
(3 Marks)
QUESTION TWO (20 MARKS)
The following data was collected and organized in an effort to analyse the performance of graduates in
a Marketing company.
Sales Number of graduates
20-29 8
30-39 10
40-49 13
50-59 15
60-69 14
70-79 10
80-89 6
90-99 4
As part of the investigating team, using an assumed mean of 54.5 where appropriate, you are required
to calculate:
a) Quartile deviation (6 Marks)
b) Mode (4 Marks)
c) Standard deviation (6 Marks)
d) Coefficient of variation (4 Marks)
3
QUESTION THREE (20 MARKS)
a) Explain the following terms
i) Regression
ii) Correlation
iii) Correlation coefficient ( 6 Marks)
b) The following table show the marks denoted by x and y respectively of 10 students on two school
quizzes in introduction to computers:
Quiz (x) 7 9 4 10 6 7 8 8 5 6
Quiz (y) 6 8 6 10 8 5 10 7 7 8
i) Construct a scatter diagram for the data. (4 Marks)
ii) Find the least square regression line of x on y and fit it in your diagram of part (i)
(10 Marks)
QUESTION FOUR (20 MARKS)
a) Explain the meaning of the following terms as used in decision theory.
i) Acts
ii) States of nature
iii) Action space
iv) Decision making (4 Marks)
b) A businessman has three alternatives open to him each of which can be followed by any of the
possible events. The conditional payoffs (in sh.) for each action is given below
Determine which alternative the businessman should choose, if he adopts the:
i) Maximin criterion. (2 Marks)
ii) Maximax criterion. (2 Marks)
iii) Hurwicz criterion, his degree of optimism being 0.65. (3 Marks)
c) The following figures show the mean market prices of three major categories of
livestock and the number sold for the years 2006 and 2007.
Payoffs conditional events
Livestock
Price (Ksh.) No. sold
2006 2007 2006 2007
Cattle 5750 6250 24900 24500
Goat 1200 1300 8700 9200
Sheep 1250 1350 2400 2900
From the data above and using 2006 as the base year calculate:
i) Laspeyre’s price index
ii) Paasches price index
iii) Fisher’s ideal index number
(9 Marks)
QUESTION FIVE (20 MARKS)
a) Explain any three factors highlighting the importance of time series analysis to a
businss organization. (3 Marks)
b) The quality control assistant tested two yarns A and B of the same count for their strength. The
following results were obtained;
Yarn A Yarn B
Number in the sample 10 15
Mean 45 55
Standard deviation 7 6
i) Determine whether or not the difference between the two yarns is significant
at 95% level of confidence. (5 Marks)
ii) For each yarn test the hypothesis that it’s mean strength is 50 at 99% level of
confidence (8 Marks)
c) Find the probability that a single toss of a die resulted in a number less than 4 if
i) No other information is given.
ii) It is given that the toss resulted in an odd number. (4 Marks)
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