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Cms 105 Introduction To Business Statistics Exam Question Paper
Cms 105 Introduction To Business Statistics Exam
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2012
1
UNIVERSITY EXAMINATIONS: 2011/2012
YEAR I EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 105 INTRODUCTION TO BUSINESS STATISTICS EXAM
(SUNDAY)
DATE: APRIL 2012 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. Descriptive Statistics and Inferential statistics (2 Marks)
ii. Skew ness and Kurtosis (2 Marks)
(b) Briefly explain the importance of time series analysis to a business organization. (6 Marks)
(c) The probability that a contractor will get a plumbing contract is 3
2 and the probability that he
will not get an electric contract is 9
5 . If the probability of getting at least one contract is 5
4 ,
what is the probability that he will get both? (4 Marks)
(d) A study by the Coca-Cola Company showed that the typical Kenyan adult consumes 18 gallons
of Coca-Cola each year. According to the same survey, the standard deviation of the number of
gallons consumed is 3.0. A random sample of 64 college students showed they consumed an
average (mean) of 17 gallons of cola last year. At the 0.05 significance level, can we conclude
that there is a significance difference between the mean consumption rate of college students and
adults? (5 Marks)
2
(e) The following marks belong to 99 students of a secondary school in Keroka Municipality
Marks Number of students
0 – 10
10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
10
x
25
30
y
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 (2 Marks)
v. Compute the coefficient of skewness (2 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 manufacturer of automobile seats has a production line that produces an average of 100 seats
per day. Because of new government regulations, a new safety device has been installed, which
the manufacturer believes will reduce average daily output. A random sample of 15 days output
after the installation of the safety device is shown below:
93, 103, 95, 101, 91, 105, 96, 94, 101, 88, 98, 94, 101, 92, 95
Assuming that the daily output is normally distributed, is there sufficient evidence at the 5%
significance level, to conclude that average daily output has decreased following the installation of
the safety device? (8 Marks)
3
QUESTION THREE
a) Using relevant examples, describe the four levels of measurement used in statistics (6 Marks)
b) Students in the CMS 105 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
12
18
26
19
20
23
15
22
8
93
57
55
90
82
95
95
80
85
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 correlation of coefficient and coefficient of determination and interpret
them. (4 Marks)
QUESTION FOUR
(a) Briefly explain four limitations of consumer index numbers. (6 Marks)
(b) A company produces 1000 refrigerators a week at three plants. Plant A produces 350
refrigerators a week. Plant B produces 250 refrigerators per week and plant C produces 400
refrigerators a week. Production records indicate that 5% of the refrigerators produced at plant A
will be defective, 3% of those produced at plant B will be defective and 7% of those produced at
plant C will be defective. All the refrigerators are shipped to a central warehouse. If a refrigerator
at the warehouse is found to be defective, what is the probability that it was produced at plant A?
(6 Marks)
4
(c) The following data relates to the prices and quantities of three commodities in the years 2001 and
2005.
Commodity
2001 2005
Price Quantity Price Quantity
A
B
C
65
95
150
20
8
5
135
160
320
30
3
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 Marks)
ii. Paasche’s index number, (2 Marks)
iii. Fisher’s ideal index number (2 Marks)
iv. Marshall-Edgeworth index number. (2 Marks)
QUESTION FIVE
(a) Differentiate between the following terms as used in statistics (2 Marks)
i. Type I error and Type II error
ii. Two tailed test and one tailed tests (2 Marks)
(b) The national Oil Corporation is considering whether to go for an offshore drilling contract. If they
bid, the value would be Sh. 600 million with 65% chance of gaining the contract. The corporation
may set up a new drilling operation or move already existing operation, which has proved
successful, to new site. The probability of success and expected returns are as follows:
Outcome
New drilling operation Existing operation
Probability Expected Revenue
(Sh. Million)
Probability Expected Revenue
(Sh. Million)
Success
Failure
0.75
0.25
800
200
0.85
0.15
700
350
If the corporation does not bid or lose the contract, they can use Sh. 600 million to modernize their
operations. This would result in a return of either 5% or 8% on the sum invested with probabilities
0.45 and 0.55 respectively. Required:
i. Construct a decision tree for the problem showing clearly the courses of action.
(10 Marks)
ii. Determine the corporation’s optimal strategy. (6 Marks)
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