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Cms 301: Advanced Business Statistics (Sunday Class) Question Paper
Cms 301: Advanced Business Statistics (Sunday Class)
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2009/2010
THIRD YEAR STAGE I EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 301: ADVANCED BUSINESS STATISTICS (SUNDAY CLASS)
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE 30 MARKS (COMPULSORY)
(a) Define the following terms as applied in statistics:
(i) Statistical quality control [2 Mark]
(ii) Decision making under risk [2 Mark]
(iii) Multivariate linear correlation [2 Mark]
(iv) Sampling strategy [2 Mark]
(b) The following data gives the number of defectives in 4 independent samples from a production
process. The samples are of varying sizes.
Sample
number
Sample size Number of
defectives
1 20 20
2 10 90
3 15 50
4 50 40
Construct a p-chart. [6 Marks]
2
(c) The time between two arrivals at a queuing system is normally distributed with mean of 2 minutes
and standard deviation of 0.25 minute. If a random sample of 36 is drawn, find the probability that
the sample mean will be greater than 2.1. [5 Marks]
(d) The following table relates to the age of employees and the number of days they reported sick in a
month.
Employees: 1 2 3 4 5 6 7 8 9 10
Age: 30 32 35 40 48 50 52 55 57 61
Sick days: 1 0 2 5 2 4 6 5 7 8
Calculate
Karl Pearson’s Coefficient of correlation and interpret your results. [9 Marks]
QUESTION TWO 20 MARKS
(a) The following table gives production of maize in a given province of a period of 10 years.
Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Production(‘000
tones
21 22 23 23 24 22 25 26 27 26
Calculate:
(i) 3-yearly moving totals [1 Mark]
(ii) 3-yearly moving average [3 Marks]
(iii) 4- yearly moving average [3 Marks]
(iv) Semi-moving average [3 Marks]
(b) In the year 2000 a firm began down sizing in order to reduce its costs. One of the results of these
cost cutting measures has been a decline in the percentage of private industry jobs that are
managerial. The following data show the percentage of females who are managers from 2000 to
2007.
(i) Develop a linear trend line for this time series through 2005 only. [7 Marks]
(ii) Use this trend to estimate the percentage of females who are manages in 2008
Years
2000 2001 2002 2003 2004 2005 2006 2007
Percentage
5.9 5.1 4.2 6.3 6.0 7.4 5.3 6.0
3
[3 Marks]
QUESTION THREE 20 MARKS
(a) 1000 light bulbs with mean life of 120 days are installed in a new factory and their length of life is
normally distributed with standard deviation of 20 days. Find how many bulbs will expire in less
than 90 days [5 Marks]
(b) A businessman has Ksh 10,000 to invest in one of the three options A, B and C. The return on is
investment depends on whether the economy experiences inflation, recession or no change at all.
His possible returns under each economic condition are given below.
State of Nature
Strategy Inflation Recession No change
A 2000 1100 1300
B 3200 600 1000
C 2300 900 1800
Establish her decision using
(i) Pessimistic criterion [2 Marks]
(ii) Optimistic criterion [3 Marks]
(c) The probability of the demand for Lorries for hiring on any day in a given district is as follows;
Number of lorries demanded 0 1 2 3 4
Probability 0.1 0.2 0.3 0.2 0.2
Lorries have a fixed cost of Kshs 8,000 each day to keep the daily hire charges (net of variable costs of
running) Kshs 15,000. If the lorry hire company owns 4 Lorries,
(i) what is its daily expectations [4 Marks]
(ii) Suppose the company is about to go into business and currently has no Lorries, calculate
the number of Lorries it should buy to maximize its profits. [6 Marks]
QUESTION FOUR 20 MARKS
(a) Explain any two methods used in statistical forecasting [4 Marks]
4
(b) A sample survey of 6 families was taken and the figures obtained with respect to three variables of
interest are given in the table.
1 x 2 x 3 x
4 15 30
6 12 24
7 8 20
9 6 14
13 4 10
15 3 4
(i) Fit the least – square regression equation of 1 x on 2 x and 3 x [8 Marks]
(ii) Estimate 1 x given that 2 x =22 and 3 x =20. [2 Marks]
QUESTION FIVE 20 MARKS
(a) Differentiate between a P- chart and a C- Chart. [4 Marks]
(b) Explain the main steps in constructing a control chart for dispersion (R- Chart) [6 Marks]
(c) Differentiate between producers risk and Consumer risk as used in statistical quality control
[2 Marks]
(d) A machine is set to deliver packets of a given weight. Ten samples of size 5 were recorded. Below
are the given relevant data
Sample
numbers
1 2 3 4 5 6 7 8 9 10
Mean 15 17 15 18 17 14 18 15 17 16
Range 7 7 4 9 8 7 12 4 11 5
Calculate the value of the central limits for the mean chart and range chart and then comment on the
state of control (conversion factors for n=5 are A2=0.58, D3=0, and D4=2.115).
[8 Marks]
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