Get premium membership and access revision papers, questions with answers as well as video lessons.
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: 2009/2010
THIRD YEAR STAGE I EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 301: ADVANCED BUSINESS STATISTICS (EVENING)
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE (30 MARKS)
(a). Giving an example, discuss the following sampling techniques
(i) Probability sampling [5 Marks]
(ii) Non-Probability sampling [5 Marks]
(b) The data in the table below relates to the weekly maintenance cost (Kenya pounds) to the age (in
months) of ten machines of similar type in a manufacturing company.
Machine 1 2 3 4 5 6 7 8 9 10
Age (x) 5 10 15 20 30 30 30 50 50 60
Cost (y) 190 240 250 300 310 335 300 300 350 395
(i) Fit the least square regression line of maintenance cost on age [6 Marks]
(ii) Predict the maintenance cost for a machine of this type which is 40 months old. [2 Marks]
(c) In a certain sampling inspection, the number of defectives found in 10 samples of 100 each are
as given below;
16, 18, 11, 18, 21, 10, 20, 18, 17 and 21. Do these indicate that the quality characteristic is under
statistical control? [6 Marks]
(d) On the basis of observations made on 39 cotton plants, the correlation of yield of cotton ( ) 1 X ,
number of bolls ( ) 2 X and height ( ) 3 X are found to be:
0.7, 12 r = 0.61, 13 r = 0.4 23 r = ,
Find the value of
(i) 23.1 r [3Marks]
2
(ii) 13.2 r [3Marks]
QUESTION TWO (20 MARKS)
(a) Explain the following terms as used in decision theory
(i) Decision alternatives [2 Marks]
(ii) Expected Monetary Value (EMV) [2 Marks]
(iii) Payoff [2 Marks]
(b) Ms Otto has Ksh 20,000 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 1200 1500
B 3000 800 1000
C 2500 1000 1800
Establish her decision using
(i) Minimax criterion [2 Marks]
(ii) Maximax criterion [2 Marks]
(c) A physician purchases a particular vaccine on Monday each week. The vaccine must be used
within the following week, otherwise it becomes worthless. The vaccine costs US$ 2 per dose and the
physician charges US$4 per dose. In the past 50 weeks, the physician has administered the vaccine in
the following quantities:
Doses per week 20 25 40 60
Number of weeks 5 15 26 5
(i) Construct the conditional profit value for the problem [3 Marks]
(ii) Construct a pay off table for the above problem [4 Marks]
(iii) Determine how many doses the physician should buy every week. [3 Marks]
QUESTION THREE (20 MARKS)
(a) Explain any two methods used in statistical forecasting [2 Marks]
(b) 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:
3
Family Annual
Savings ( 1 x )
Annual
Income ( 2 x )
Family
size ( 3 x )
1 10 16 2
2 4 13 6
3 5 15 5
4 8 13 3
(i) Fit the least – square regression equation of 1 x on 2 x and 3 x [7 Marks]
(ii) Estimate 1 x given that 2 x =11,000 and 3 x =8. [2 Marks]
(c) The table below gives prices of tea and coffee of a given quantity meant for an export market
Price of tea
(Kshs‘000)
75 88 95 70 60 80 81 50
Price of coffee
(Kshs‘000)
120 134 150 115 110 140 142 100
Calculate the coefficient of correlation using the Spearman’s Rank correlation method [5Marks]
d) Explain two advantages and two limitations of multiple correlation analysis. [4 Marks]
QUESTION FOUR (20 MARKS).
(a) Explain the three main steps in constructing a control chart for dispersion (R- Chart) [3 Marks]
(b) Eight samples of size three each are drawn at regular intervals from a manufacturing process. The
data is given in the table below
Sample
Number
Observations
1 32 37 42
2 28 32 40
3 39 52 28
4 50 42 45
5 42 45 34
6 50 29 21
7 44 52 35
8 22 35 44
Construct
(i) the mean chart [4Marks]
(ii) the range chart [3Marks]
(iii) Comment on the state of control [1 Mark]
N/B: (conversion factors for n=3 are A3=1.023, D3=0, and D4=2.575).
(c) Describe a double sampling plan [4 Marks]
4
(d) A company is producing an item whose weight is normally distributed with standard
deviations = 8 gm. Shipments averaging less than 200gm are considered poor quality and the
company would like to minimize such shipments. Design a sampling plan for a sample of size
n = 25 that will limit the risk of rejecting lots that average 200gm to 5 per cent. [5 Marks]
QUESTION FIVE (20 MARKS)
(a) Explain four advantages of Statistical Quality Control from the producer’s point of view.
[4Marks]
(b) A banker has studied his record and notices that for the past 300 days in the year, the demand
for his product has varied as follows:
Demand (‘000 units) 5 6 7 8 9
Number of days 20 60 80 120 20
Find the expected demand for his product [2Marks]
(c) The following table gives production of maize in a given province of a period of 10 years.
Year 200
0
200
1
200
2
200
3
200
4
200
5
200
6
200
7
200
8
Production(‘0
00 tones
21 22 23 23 24 22 25 26 27
Calculate:
(i) 3-yearly moving totals [1 Mark]
(ii) a simple 4- yearly moving average [2 Marks]
(iii) a weighted three month moving average where the weights are highest for the latest
months and descend in order of 3,2,1 [4 Marks]
(iv) the trend using the Semi-moving average method [4 Marks]
(d) Explain three limitations of business forecasting as a tool of analyzing business data. [3 Marks]
More Question Papers
Popular Exams
Return to Question Papers