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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:2011
KIMATHI UNIVERSITY COLLEGE OF TECHNOLOGY
University Examinations 2011/2012
FIRST YEAR SECOND SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
HBC 2121 Introduction to Business Statistics
DATE: 5 TH DECEMBER 2011 TIME: 2.00 PM{4.00 PM
Instructions: Answer QUESTION ONE and any other TWO QUESTIONS.
QUESTION ONE (30 marks) (COMPULSORY)
(a). De ne the following terms as used in statistics.
(i) Nominal measurements
(ii) Ordinal measurements
(iii) Independent events
(iv) Coecient of variation
(v) Mutually exclusive events [5 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 [7 marks]
(c). The rst 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, nd the mean and
standard deviation of the second group. [5 marks]
(d). The following data refers to Examination marks verses hours of study per week of
a sample of eight candidates that sat for Business statistics examination in 2010.
1
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 coecient of correlation. [5 marks]
(ii) the coecient of determination between examination marks and hours of
study. [2 marks]
(e). If 50% of the families subscribe to the morning newspaper, 65% of the families
subscribe to the afternoon newspaper and 85% of the families subscribe to at
least one of the two newspapers, what proportion of the families subscribe to both
newspapers? [3 marks]
(f). (i) Under what conditions does P(AjB) = P(A)? [1 marks]
(ii) What is the addition rule of probability and for what type of events is it
valid? [2 marks]
QUESTION TWO (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 number. [2 marks]
(c). (i) De ne the term \time series" and giving an example. [2 marks]
(ii) What is the aim of time series analysis? [2 marks]
(iii) By giving the relevant examples, brie
y explain the components of a time
series. [6 marks]
(d). The number of new stereo systems sold by an electrical store each quarter for four
years is shown below.
Year Quarters Sales
1 130
2 105
2000 3 85
4 120
1 150
2 115
2001 3 95
4 140
1 165
2 120
2002 3 100
4 140
1 180
2 140
2003 3 110
4 160
2
Calculate a four point moving average trend. [6 marks]
QUESTION THREE (20 marks)
(a). The following table gives the marks obtained by rst year students in a Marketing
examination.
Marks 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
No. of Students 3 9 14 24 18 16 9 4
Calculate
(i) the mean
(ii) the Standard deviation
(iii) the median, and
(iv) the mode [10 marks]
(b). (i) State Bayes Theorem. [2 marks]
(ii) KY accounting rm has noticed that of the companies it audits, 85% show no
inventory shortages, 10% show small inventory shortages and 5% show large
inventory shortages. KY rm has devised a new accounting test for which it
believes the following probabilities hold:
P(company will pass test j no shortages) = 0:90
P(company will pass test j small shortages) = 0:50
P(company will pass test j large shortages) = 0:20
Determine the probability if a company being audited fails this test has large
or small inventory shortages. [8 marks]
QUESTION FOUR (20 marks)
(a). Statistics is a means of collection of numerical facts on data. What are the major
advantages of sampling method over the census? [4 marks]
(b). The random variable X has a probability distribution shown in the table below
X 0 10 20 30
P(X = x) 0.1 p 0.45 q
Given that the mean of X is 16.5, nd the value of p and q. [4 marks]
(c). The following data shows two groups of casual workers, their number and average
wages they are paid.
Group A Group B Combined Groups
Number of Workers X 100 250
Mean wage 600 Y 6800
Standard Deviation 8 9 Z
(i) Calculate the missing entries; X, Y , and Z. [8 marks]
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(ii) Calculate the coecient of variation for Groups A and B. [3 marks]
(iii) From (ii) above, which group has a greater variability in income? [1 marks]
QUESTION FIVE (20 marks)
In a study of the daily production of a company for 50 days, the following data was
obtained:
65 76 36 48 49 48 84 55 79 51
43 21 78 35 37 61 40 45 68 33
88 45 50 53 60 34 56 67 57 42
59 62 62 65 76 55 76 61 70 73
35 41 60 74 52 82 63 58 32 26
(i) Starting with a class 20??29, group the data into a frequency distribution, represent
the data in a histogram and plot its ogive. [8 marks]
(ii) State the modal class. [1 marks]
(iii) Using a suitable assumed mean, calculate the mean hence or otherwise calculate,
the mode, the median and the standard deviation of the data above. [11 marks]
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