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Cms 105: Introduction To Business Statistics. Question Paper
Cms 105: Introduction To Business Statistics.
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2008/2009
THIRD YEAR STAGE 1 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 105: INTRODUCTION TO BUSINESS STATISTICS.
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
(a) Differentiate between the following terms
(i) Descriptive statistics and inferential statistics. (2 Marks)
(ii) Skew ness and kurtosis (2 Marks)
(iii) An event and an experiment. (2 Marks)
(iv) Null hypothesis and alternative hypothesis. (2 Marks)
(v) Price index and quantity index. (2 Marks)
(b) The number of solar heating systems available to the public is quite large, and their heat
storage capacities are quite varied. Below is a distribution of heat storage capacity (in days) of
28 systems that were tested recently by a testing agent
Days Frequency Days Frequency
9.3-9.7 2 11.3-11.7 14
9.8-10.2 5 11.8-12.2 6
10.3-10.7 F3 12.3-12.7 3
10.8-11.2 F4 12.8-13.2 1
2
Given that the arithmetic mean of the data is 11.09.
Find the missing frequencies F3 and F4 respectively (Use assumed mean of 11). (5 Marks)
(c) A husband and wife appear in an interview for two vacancies in the same post. The probability
of husband’s selection is 1/7 and that of wife’s is 1/5.Find the probability
i. Both of them will be selected (2 Marks)
ii. Only one of them will be selected (4 Marks)
(d) A random sample of boots worn by 40 combat soldiers in a desert region showed an average
life of 1.08 years with a standard deviation of 0.05. Under the standard conditions, the boots
are known to have an average life of 1.28 years. Is there reason to assert at a level of
significance of 0.05 that use in the desert causes the mean life of such boots to decrease?
(5 Marks)
(e) Given the following table with states of nature as N1, N2 and N3 with strategies S1, S2 and S3
Investigate the best strategy under
(i) Maximin criterion (2 Marks)
(ii) Maximax criterion (2 Marks)
QUESTION TWO
(a) (i) Differentiate between measures of central tendency and measures of dispersion giving
an example in each case. (3 Marks)
(ii) Two automatic filling machines A and B are used to fill tea in 500 grams cartons. A
random sample of 100 cartons on each machine showed the following:
Strategies
States of Nature
N1 N2 N3
S1 7,000 3,000 1,500
S2 5,000 4,500 0
S3 3,000 3,000 3,000
3
Tea Contents (in grams) Machine A Machine B
485-490 12 10
490-495 18 15
495-500 20 24
500-505 22 20
505-510 24 18
510-515 4 13
Comment on the performance of the two machines A and B on the basis of average filling and
dispersion. (7 Marks)
(b) Differentiate between type I and type II error. (2 Marks)
(c) A company is interested in determining whether an association exists between the commuting
time of their employees and the level of stress related problems observed on the job. A study
of 116 assembly line workers reveals the following:
Commuting
Time
stress
High Moderate Low Total
Under 20 min 9 5 18 32
20-50 min 17 8 28 53
Over 50 min 18 6 7 31
Total 44 19 53 116
At a =0.01 level of significance, is there any evidence of a significant relationship between
commuting time and stress? (8 Marks)
QUESTION THREE
(a) A product is manufactured in two ways. A pilot test on 64 items from each method indicates
that the products of method 1 have a sample mean tensile strength of 106 lubes and a standard
deviation of 12 lubes, whereas in method 2 the corresponding values of the mean and standard
deviation are 100 lubes and 10 lubes respectively. Greater tensile strength in the product is
preferable. Use an appropriate large sample test of 5% level of significance to test whether or
not method 1 is better for processing the product. State clearly the null hypothesis (5 Marks)
(b) Explain five steps involved in decision making process in the context of decision theory
approach. (5 Marks)
4
(c) The manager of a flower shop promises his customers delivery within four hours on all orders.
All flowers are purchased the previous day and delivered to Mr Chero by 8.00 am every
morning. The daily demand for the roses is as follows
The manager purchases roses for US$ 10 per dozen and sells them for US$ 30. All unsold roses
are donated to a local hospital.
i. How many dozens of roses should Mr. Chero order each evening to maximize his
profits? (8 Marks)
ii. What is the optimal expected profit? (2 Marks)
QUESTION FOUR
(a) Define the following terms
(i) Conditional probability (1 Mark)
(ii) Skew ness (1 Mark)
(iii) Kurtosis (1 Mark)
(b) The data below show the profit realized by 40 medium sized companies for the year 2006.
Profit in Millions
24.4 25.4 25.9 20.8 23.5
25.0 22.6 22.3 24.1 21.4
23.5 22.9 23.8 24.7 21.7
22.9 23.5 21.4 24.4 26.0
22.3 27.7 28.4 23.0 28.1
28.7 29.0 22.6 27.5 29.6
28.0 25.1 22.0 22.7 28.6
29.5 24.4 21.4 22.9 29.5
Required:
Using the inclusive form of grouping, prepare a frequency distribution table, with equal classes for
the above problem , beginning with the class 20.0-20.9
(i) Calculate Inter quartile range (3 Marks)
Dozens of roses 70 80 90 100
Probability 0.1 0.2 0.4 0.3
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(ii) Standard deviation (4 Marks)
(iii) Mode (3 Marks)
(iv) Karl Pearson’s coefficient of Skewness (3 Marks)
QUESTION FIVE
(a) Suppose an item is manufactured by three machines X, Y and Z. All the three machines have
equal capacity and are operated at the same rate. It is known that the percentages of defective
items produced by X, Y, and Z are 4, 14 and 24 per cent respectively. All the items produced
by X, Y , and Z are put into one bin. From this bin, one item is drawn and is found to be
defective. What is the probability that this item was produced on Y? (5 Marks)
(b) (i) Differentiate between Paasches’s index and Laspeyre’s index (2 Marks)
(ii) Calculate Fisher’s ideal index from the data given below
(6 Marks)
(c) The personnel manager of an electronic manufacturing company devices a manual test for job
applicants to predict their production rating in the assembly department. In order to do this, he
selects a random sample of 10 applicants. They are given the test and later assigned a
production rating. The results are as follows:
Worker A B C D E F G H I J
Test score 53 36 88 84 86 64 45 48 39 69
Production rating 45 43 89 79 84 66 49 48 43 76
Find the regression equation of production rating on the test score. (7 Marks)
Commodity
Base Year, 2000 Current Year, 2001
Price Value Price Value
A 10 30 12 48
B 15 60 15 75
C 5 50 8 96
D 2 10 3 25
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