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Cms 301: Advanced Business Statistics Question Paper
Cms 301: Advanced Business Statistics
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2008/2009
THIRD YEAR STAGE 1 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 301: ADVANCED BUSINESS STATISTICS
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE (30 MARKS)
(a) Define the following terms as applied in statistics
(i) Probability sampling
(ii) Decision making under risk
(iii) Statistical Quality Control
(iv) Expected Monetary Value
(v) Forecasting
(10 Marks)
(b) A manufacturing process produces ball bearings with mean 5 cm and standard deviation of 0.005
cm. A random sample of 9 bearings is selected to measure their average diameter. This is found to
be 5.004 cm. What is the probability that the average diameter of 9 randomly selected bearings
would be at least 5.004 cm? (5Marks)
(c) A machine is set to deliver packets of a given weight. Ten samples of size 5 each were recorded as
shown below:
Sample
number
1 2 3 4 5 6 7 8 9 10
Sample mean 12.8 13.1 13.5 12.9 13.2 14.1 12.1 15.5 13.9 14.5
Calculate the value for the central line and the control limits for the mean chart. (5 Marks)
2
(d) The general manager of a building materials production plant feels that the demand for
plasterboard shipments may be related to the number of construction permits issued in the country
during the previous quarter. The manager has collected the data below
(i) Use the normal equations to derive a regression forecasting ( 6 Marks)
(ii) Determine a point estimate for plasterboard shipments when the number of
construction permits is 30. (2 Marks)
(e) Differentiate between a P- chart and a C- Chart. (2 Marks)
QUESTION TWO
(a) Differentiate between the following terms
(i) Process control and control chart (4 Marks)
(ii) Attribute plan and variable plan (4 Marks)
(b) Explain four steps in setting up a control procedure (4 Marks)
(c) The following data gives the number of defectives in 5 independent samples from a
production process. The samples are of varying size.
Sample
number
Sample size Number of
defectives
1 2000 400
2 1000 150
3 1000 120
4 600 80
5 400 50
total 5000 800
Draw the p-chart (fraction defective chart) (8 Marks)
QUESTION THREE
(a) Explain the following terms as used in decision theory
(i) Decision alternatives (2 Marks)
(ii) State of nature (2 Marks)
(iii) Payoff (2 Marks)
Construction permits 15 9 40 20 25 25 15 35
Plasterboard shipments 6 4 16 6 13 9 10 16
3
(b) By giving examples explain any four types of Probability sampling techniques (4 Marks)
(c) A sample survey of 4 families was taken and the figures obtained with respect to their annual
savings 1 x (in Kshs 100’s), annual income 2 x (in Kshs 1000’s), and family size 3 x . The data
is:
Family Annual
Savings ( 1 x )
Annual
Income ( 2 x )
Family
size ( 3 x )
1 10 14 4
2 7 12 6
3 2 10 5
4 8 14 4
(i) Fit the least – square regression equation of 1 x on 2 x and 3 x (7 Marks)
(ii) Estimate the annual income of a family whose annual savings is 5,500 and
whose members (size) are 4. (3 Marks)
QUESTION FOUR
(a) A grocery with a bakery department is faced with a problem of how many cakes to buy in
order to meet the day’s demand. The grocer prefers not to sell day-old goods in competition
with fresh products. Leftover cakes are therefore, a complete loss. On the other hand, if a
customer desires a cake and all of them have been sold, the disappointed customer will buy
from elsewhere and the sale will be lost. The grocer has, therefore, collected information on
the past sales on a selected 100 day period as shown below:
If a cake costs Kshs 80.00 and sells for Kshs 100.00
i. Construct the payoff table and the opportunity loss table. (8 Marks)
ii. Find the optimal number of cakes that must be bought per day (2 Marks)
(b) Explain the Five steps in constructing a C- Control Chart (5 Marks)
(c) Twenty tape recorders were examined for quality control tests. The number of defects for
each tape recorder is given below
2,4,3,1,1,2,5,3,6,7,3,1,4,2,3,1,6,4,1,1,
Sales Number of Days Probability
25 10 0.1
26 30 0.30
27 50 0.50
28 10 0.10
4
Prepare a C-chart. State whether the process in under control or not. (5 Marks)
QUESTION FIVE (20 MARKS)
(a) 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)
(b) Define the following terms:
i. Time series ( 2 Marks)
ii. Moving average (2 Marks)
(c) A state government is studying the number of traffic fatalities in the state resulting from
drunken driving for each of the last 12 months.
Month 1 2 3 4 5 6 7 8 9 10 11 12
Accidents 280 300 280 280 270 240 230 230 220 200 210 200
Find the trend line that describes the trend by using the method of semi-averages (4 Marks)
(d) A machine is set to deliver packets of a given weight. Ten samples of size 5 were recorded as
shown below.
Sample
numbers
1 2 3 4 5 6 7 8 9 10
Range 2.1 3.1 3.9 2.1 1.9 3.0 2.5 2.8 2.5 2.0
Calculate the values of the central line for the range chart and then comment on the state of
control (conversion factors for n=5 are A2=0.577, D3=0, and D4=2.115). (5 Marks)
(e) Differentiate between producers risk and Consumer risk as used in statistical quality control
(2 Marks)
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