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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 EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 105: INTRODUCTION TO BUSINESS STATISTICS – Sunday
DATE: AUGUST 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE (30 MARKS)
a) The following data has been collected with the intention of determining whether there should be
need of concern of performance discrepancies among the staff in the marketing department of a
company. To reach a decision it is required to know the mean and standard deviation of the
collected data below. Compute these parameters to the accuracy of one decimal place.
200, 195, 203, 200, 197, 205, 200, 198, 201, 204, 203. (5 Marks)
b) The mean lifetime of 91 light tubes produced by accompany is found to be 1610 hours with
standard deviation of 80 hours. Test the hypothesis that the mean lifetime of the tubes produced by
the company is 1600 hours at 99% level of confidence. (5 Marks)
c) Calculate the rank correlation coefficient for the following data of two tests given to candidates for
a clerical job.
Test 1 76 83 80 79 65 81
Test 2 80 79 85 60 64 58
(5 Marks)
d) A businessman has three alternatives A1, A2 and A3 open to him each of which can be followed
by any of the possible events N1, N2 and N3. The conditional payoffs (in sh.) for each actionevent
combination is given below
2
Determine which alternative should the businessman choose, if he adopts the
i) Maximax criterion (2 Marks)
ii) Hurwicz criterion, his degree of optimism being 0.7 (4 Marks)
e) Calculate the aggregate price index and comment on the cost of living index based on the following
data provided about five basic items.
2008 2009
ITEM Weight Price Price
A 2 20 27
B 2 30 43
C 4 10 15
D 5 15 23
E 3 22 25
(5 Marks)
f) As a member of an organizations top management, you are so frequently involved in decision
making.
i) Outline the five steps of a decision making process. (2 Marks)
ii) Give three methods of decision making under uncertainty. (2 Marks)
QUESTION TWO (20 MARKS)
a) Define the following terms as used in decision theory:
i) Action space
ii) State of nature
iii) Out comes
iv) Pay-off
(4 Marks)
b) Calculate the Karl Pearson’s coefficient of correlation for the following set of data. (10 Marks)
Supply 15 18 20 24 30 35 40 45
Demand 85 93 95 105 120 130 150 160
Alternative Payoffs conditional events
N1 N2 N3
A1
A2
A3
6500
4500
2500
2500
4000
2500
1000
500
2500
3
c) The frequency table below gives scores obtained by 50 students in a statistics test at KCA
University.
Calculate the coefficient of kurtosis for the data and comment (6 Marks)
QUESTION THREE (20 MARKS)
a) Compute the population mean interval if a random sample of 81 specimens gave a mean of 190 and
standard deviation of 18 at 95% confidence level. (5 Marks)
b) A product is manufactured in two ways. A test on 121 items from each method indicates that the
products of method 1 have a sample mean tensile strength of 106 units and a standard deviation of
12. Whereas in method 2 the corresponding value of the mean and starndard deviation are 100 and
10 respectively. Are the two mehods significantly different at
i) 95% confidence level.
ii) 99% confidence level. (8 Marks)
c) Compute five year moving average for the following data relating to production of a commodity
and draw the trend and actual graph on same axes.
Year Production (1000 tonnes)
1999 815
2000 885
2001 775
2002 781
2003 841
2004 765
2005 810
2006 820
2007 845
2008 780
(7 Marks)
QUESTION FOUR (20 MARKS)
a) Differentiate the following terms:
i) Skewness and kurtosis
ii) Type I error and Type II error
Marks 0-4 5-9 10-12 15-19 20-24 25-29 30-34 35-39
Frequency 1 2 8 11 14 8 4 2
4
iii) Experiment and Event
(6 Marks)
b) A random sample was taken of 100 candidates who had submitted scripts at a certain examination.
The results obtained were as follows.
Marks Number of Candidates
20-30 3
30-40 9
40-50 20
50-60 34
60-70 25
70-80 7
80-90 2
Determine
i. The mode (3 Marks)
ii. The 50th percentile (3 Marks)
iii. Interquartile range (4 Marks)
iv. Standard deviation (4 Marks)
QUESTION FIVE (20 MARKS)
a) From the data below and using 2005 as the base year calculate for both 2006 and 2007:
i) Laspeyre’s price index
ii) Paasches price index
iii) Fisher’s index number
2005 2006 2007
ITEM Price Quantity Price Quantity Price Quantity
A 2 30 3 30 5 28
B 3 15 5 20 6 25
C 10 4 15 8 3 6
(15 Marks)
b) The probability that a contractor will get a plumbing job is 3
1 and the probability that he will not
get an electric contract is 8
3 . If the probability of getting at least one job is 7
5 , find the
probability that he gets both contracts. (5 Marks)
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