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Introduction To Business Statistics (Sunday) Question Paper
Introduction To Business Statistics (Sunday)
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 105 : INTRODUCTION TO BUSINESS STATISTICS (SUNDAY)
DATE: AUGUST 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
Question One
(a)Differentiate between the following terms as used in statistics:-
i. Mutually exclusive events and Independent events [2 Marks]
ii. Descriptive statistics and Inferential Statistics [2 Marks]
(b)Given below are the data on a sample of 30 annual incomes (in Sh. 000)
19.1 19.8 18.0 19.2 19.5 17.3
20.0 20.3 19.6 18.5 18.1 19.7
18.4 17.6 21.2 19.7 22.2 19.1
21.1 19.3 20.8 21.2 21.0 18.7
19.9 18.7 22.1 17.2 18.4 21.4
Construct a stem and leaf display for these data [3 Marks]
(c)Briefly explain four factors to consider when constructing index numbers [4 Marks]
(d)KK accounting firm has noticed that of the companies it audits, 85% show no inventory shortages,
10% show small inventory shortages and 5% show large inventory shortages. KK firm has devised
a new accounting test for which it believes the following probabilities hold:-2
P (company will pass test / no shortage) = 0.90
P (company will pass test / small shortage) = 0.50
P (company will pass test / large shortage) = 0.20
Required:
i. Determine the probability that if a company being audited fails this test it has a large or a small
inventory shortage [3 Marks]
ii. If a company being audited passes this test, what is the probability of no inventory shortage?
[3 Marks]
However, it was possible to ascertain that the total number of frequencies was 150 and that the median
has been correctly found out as 146.125
Required:-
i. Determine the missing frequencies [3 Marks]
ii. Calculate the arithmetic mean [2 Marks]
iii. The standard deviation [2 Marks]
iv. Coefficient of skewness [2 Marks]
(f) The manager of a departmental store is thinking about establishing a new billing system for the
stores credit customers. After a thorough financial analysis, she determines that the new system will not be cost effective if the average monthly account is less than 70,000. A random sample of 200 monthly accounts is drawn, for which the mean monthly account is Sh. 66,000. With a = 0.05,
is there sufficient evidence to conclude that the new system will not be cost effective? Assume that
the population standard deviation is Sh. 30,000. [4 Marks]
Question Two
(a) Briefly explain the three approaches of assigning probabilities [3 Marks]
From the above data, calculate the Fisher’s ideal price index numbers for 2010 taking 2005 as
the base year [5 Marks]
(d) A highway patrol officer believes that the average speed of cars traveling on a certain stretch of
highway exceeds the posted limit of 55 km/ hr. A random sample of 10 cars had their speeds
measured by radar. The results in km / hr are as follows:
71, 53, 62, 49, 59, 52, 58, 61, 85, 55
Do these data provide sufficient evidence to support the highway patrol belief, at the 5% level of
significance? [7 Marks]
Question Three
(a)Briefly explain the three types of decision –making environments [3 Marks]
(b)A factory produces a component that is used in manufacturing computers. Each component is tested
prior to shipment to determine whether or not it is defective. In a random sample of 250 units, 20 were found to be defective. Estimate with 99% confidence the true proportion of defective components produced by the factory. [4 Marks]
(c)Briefly explain FOUR reasons for sampling in statistics [4 Marks]
(d)A firm has developed a new product X. They can either test the market or abandon the project. The
details are set out below;
Test market cost Sh. 50,000. Likely outcomes are favourable (P = 0.7) or failure (P = 0.3). If favourable, they could either abandon or produce it when demand is anticipated to be: -
Low P = 0.25 Loss Sh. 100,000
Medium P = 0.6 Profit Sh. 150,000
High P = 0.15 Profit Sh. 450,000
If the test market indicates failure, the project would be abandoned. Abandonment at any stage results in a gain of sh.30, 000 from the special machinery used.
Required:
i. Draw a decision tree for the above problem, including all the relevant data. [5 Marks]
ii. Using expected values, analyze the decision tree and recommend the best option to the managers
of the firm. [4 Marks]
Question Four
(a) Using appropriate examples, describe the levels of measurement used in statistics [6 Marks]
(b)The different interest rates charged by some financial institutions may reflect how stringent their
standards are for their loan appraisals i.e. the lower the rate, the higher the standards and hence the
lower the default rate. The following data were collected from a sample of nine financial
companies selected at random.
Interest rate (%) X 7.0 6.6 6.0 8.5 8.0 7.5 6.5 7.0 8.0
Default rate (per 1000 loans) Y 38 40 35 46 48 39 36 37 44
Required:
i. Find the least squares regression line that can be used to estimate the default rate given that
the interest rate is known [8 Marks]
ii. Interpret the values of the constants calculated in (i) above. [2 Marks]
iii. Calculate the coefficient of correlation and the coefficient of determination and interpret their
values [4 Marks]
Question Five
(a)Differentiate between the additive and the multiplicative models as used in time series analysis
[2 Marks]
(b)Briefly explain four methods of measuring the trend in time series analysis [6 Marks]
(c)The data below relates to the sales revenue of a given firm for the last three years;-
Sales Revenue (sh’ ‘000’)
Calculate the centred four- quarterly moving trend for the above data [6 Marks]
(d)A firm has four plants (A, B, C and D) scattered around the city producing the same homogeneous
item at all the plants. Plant A produces 30% of the total production, second plant B 25%, Plant C
35% and the Plant D 10%. The firm has a single warehouse in the city for storing the finished
product of all the plants without any distinction. From the past performance records on the
proportion of defectives, it has been found that 5%, 10%, 15% and 2% of the items produced at
plants A, B, C and D respectively are defective. Before the shipment of the items to a dealer, one
unit is selected and found to be defective. What is the probability that the item was produced in
plant C? [6 Marks]
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