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Hbc 2121 Introduction To Business Statistics Question Paper
Hbc 2121 Introduction To Business Statistics
Course:Bachelor Of Commerce
Institution: Dedan Kimathi University Of Technology question papers
Exam Year:2014
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DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
University Examinations 2014/2015
FIRST YEAR SECOND SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE AND BACHELOR OF BUSINESS
ADMINISTRATION
HBC 2121 INTRODUCTION TO BUSINESS STATISTICS
DATE: APRIL 2014 TIME: 2 HOURS
Instructions:
1. Answer QUESTION ONE and any other TWO QUESTIONS.
2. Show clearly your work and the number of questions attempted.
QUESTION ONE [30 MARKS]
a) Differentiate the following terms as used in statistics.
i. Independent events and mutually exclusive events [2 Marks]
ii. Continuous variables and discrete variables [2 Marks]
b) The Marks obtained by 30 students in a mathematics test marked out of 20 are as shown
below
Marks 8 9 10 11 12 14 15 17 18 20
No. of
students
2 3 4 4 5 3 3 3 2 1
Compute.
i. The mode
ii. Median
iii. Mean
iv. Standard deviation [8 Marks]
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c) The first of the two groups has 100 items with mean 45 and variance 49. If the combined
group has 250 items with mean 51 and variance 130. Find the mean and standard
deviation of the second group. [5 Marks]
d) The following data refers to examination Marks versus hours of study per week of a
sample of eight candidates that sat for business statistics examination in 2010.
Exam
mark(Y)
64 61 84 70 88 92 72 72
Hours of
study(X)
20 16 34 23 27 32 18 22
Calculate:
i. The Pearson’s product moment of correlation [5 Marks]
ii. The coefficient of determination between examination Marks and hours of study.
[2 Marks]
e) If 50% of families subscribe to the morning paper, 65%of the families subscribe to the
afternoon paper and 85% of these families subscribe to at least one of the two newspapers,
what proportion of the families subscribe to both newspapers. [3 Marks]
f) Under what condition does P(A/ B) ? P(A) ? [1 Mark]
g) What is the addition rule of probability and for what type of events is it valid?
[2 Marks]
QUESTION TWO (20 MARKS)
a) A battery manufacturer was interested in predicting the annual maintenance cost of the
battery manufacturing machines based upon the age of the machine. A sample of ten
machines revealed the following ages and maintenance costs during the previous year.
Age years) 9 4 2 8 4 5 1 3 6 8
cost 40 12 8 27 15 17 5 10 25 31
i. Define regression analysis [1 Mark]
ii. Fit the linear regression model to the data using the least squares method.
[7 Marks]
iii. Interpret the meaning of the slope in the linear regression model in part (ii)
[1 Mark]
iv. Predict the maintenance cost of a machine that is 10 years old. [1 Mark]
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b) An aircraft emergency locator transmitter (ELT) is a device designed to transmit a signal
in the case of a crash. The Ultimate manufacturing company makes 80% of the ELTs, the
Bryant Company makes 15% of them, and the Charter air company makes the other 5%.
The ELTs made by Ultimate have a 4% rate of defects; the Bryant ELTs have a 6% rate
of defects, and the Charter air ELTs have 9% rate of defect (Which helps to explain why
charterair has the lowest market share). An ELT is randomly selected from the general
population of all ELTs then tested and is found to be defective.
i) Find the probability that the ELT is defective. [4 Marks]
ii) If a randomly selected ELT is defective, find the probability that it was made by
the ultimate manufacturing company [3 Marks]
iii) If a randomly selected ELT is defective, find the probability that it was made by
the charterair manufacturing company. [3 Marks]
QUESTION THREE (20 MARKS)
a) What is an index number? Explain two areas where index numbers are applied.
[2 Marks]
b) If the Fisher’s price index is 109.91 and the Paasche’s price index is 110.6,
calculate the Laspeyre’s index. [2 Marks]
c) Define the term “time series” and give an example [2 Marks]
d) What is the aim of time series analysis [2 Marks]
e) By giving relevant examples briefly explain the components of a time series.
[6 Marks]
f) The number of new stereo systems sold by an electrical store each quarter for four
years is shown below.
year quarters sales
2000 1
2
3
4
130
105
85
120
2001 1
2
3
150
115
95
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4 140
2002 1
2
3
4
165
120
100
140
2003 1
2
3
4
180
140
110
160
Calculate a four point moving average tread. [6 Marks]
QUESTION FOUR (20 MARKS)
a) A hospital has developed a test to discover if new born babies have a certain type of
mental disorder. From past records it is known that the probability that a baby has this
disorder is 0.003.If the baby does have the disorder, the test will be positive 98% of the
time. If the baby does not have the disorder, the test will be negative 99% of the time. The
test is administered on a newborn baby and is positive. What is the probability that the
baby has the disorder? [4 Marks]
b) “Statistical enquiries mean some sort of investigation by any agency whatsoever wherein
relevant information is collected in numbers rather than words”. Briefly explain the stages
involved in any statistical enquiry. [12 Marks]
c) Giving relevant examples distinguish between descriptive statistics and inferential
statistics. [4 Marks]
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QUESTION FIVE (20 MARKS)
a) The table below shows the prices of average person’s diet and the basket of goods in the
year 2000 and 2005.
Item Price 2000 Price 2005 Quantity 2000 Quantity 2005
Steak £2.20 £3.00 50 40
Pepper £2.00 £2.00 2 3
Bread £.50 £.60 80 100
Determine the Laspeyre’s price index, paashce’s price index and Fisher’s ideal index
[10 Marks]
b) In a study of the daily production of a company over 50 days, the following data was
obtained.
65 76 36 48 84 55 79 51 49 48
43 21 78 35 40 45 68 33 37 61
88 45 50 53 56 67 57 42 60 34
59 62 62 65 74 61 70 73 76 55
35 41 60 74 63 58 32 26 52 82
i) Starting with a class 20-29, group this data into a frequency distribution and plot
its frequency polygon. [4 Marks]
ii) Using assumed mean method (A=60.5), calculate the mean and standard deviation.
[4 Marks]
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