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Advanced Business Statistics Question Paper
Advanced Business Statistics
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2008
UNIVERSITY EXAMINATIONS: 2008/2009
THIRD YEAR STAGE 1 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 301: ADVANCED BUSINESS STATISTICS
DATE: DECEMBER 2008 TIME: 2 Hours
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
(a) Define the following terms:
(i) Forecasting [2 Marks]
(ii) Statistical quality control [2 Marks]
(iii) Decision making under risk [2 Marks]
(iv) Multivariate linear correlation [2 Marks]
(v) Sample [2 Marks]
(b) A machine is set to deliver an item of a given weight, 10 samples of size 5 each were
recorded. The relevant data were as follows:
Samples 1 2 3 4 5 6 7 8 9 10
Mean,
-x
15 17 15 18 17 14 18 15 17 16
Range (R) 7 7 4 9 8 7 12 4 11 5
(i) Calculate the values for the control limits for mean chart and the range chart
and then comment on the state of control. (Conversion factors for n=5 are
A2=0.58,D3=0, D4=2.115) [6 Marks]
2
(ii) Comment on your results. [2 Mark]
(c) Find the coefficient of correlation between the following data
Cost 39 65 62 90 82 75 25 98 36
78
Sales: 47 53 58 86 62 68 60 91 51
84
[6 Marks]
(d) The following is a payoff (in ‘000 Kshs) for three styrategies and three states of
nature.
Strategies States of nature
N1 N2 N3
S1 700 300 150
S2 500 450 0
S3 300 300 300
Determine the optimal decision under each of the following criteria
(i) Maximax [3 Marks]
(ii) Maximin [3 Marks]
QUESTION TWO
(a) Define the following terms:
i) Consumer’s risk [2 Mark]
ii) Producer’s risk [2 Mark]
iii) Lot tolerance percent defective (LTPD) [2 Mark]
(b) The following data refer to defects found at the inspection of the first 10 samples
of size 100.
Samples 1 2 3 4 5 6 7 8 9 10
No. of defectives 2 1 1 3 2 3 4 2 2 0
3
(i) Obtain the upper and lower control limits for percentage defective in samples of
100. [5 Marks]
(ii) Represent the first ten sample results in the chart you prepare to show the
central line and control limits. [3 Marks]
(c) The following calculations have been made for prices of twelve stocks (x) at the
ABC stock exchange on a certain day along with the volume of sales in thousands
of shares (y). From these summations find the regression equation of price of
stocks on the volume of sales of shares.
S x =580 , S y = 370 S xy = 11494, S x2 = 41658,
S y 2 =17206
[6 Mark]
QUESTION THREE
(a) An owner of a small garment shop is hopeful that her sales are rising significantly
every week. The following data gives her record over six weeks.
Week 1 2 3 4 5 6
Sales in kshs ’000s 2.69 2.62 2.80 2.70 2.75 2.81
Calculate the Karl Pearson’s correlation coefficient and interpret your results [4 Marks]
(b) (i) Define forecasting [2 Marks]
(ii) Briefly explain any two objectives of forecasting [4 Marks]
(c) The following table gives production of maize in a given province of a period of 10
years.
4
Year Production in (‘000 tones)
1987 21
1988 22
1989 23
1990 23
1991 24
1992 22
1993 25
1994 26
1995 27
1996 26
Calculate:
(i) 3-yearly moving totals [3 Marks]
(ii) 3-yearly moving average [4 Marks]
(iii) Short term error (forecast error) [3 Marks]
QUESTION FOUR
(a) Giving examples , discuss the following sampling techniques
(i) Probability sampling [5 Marks]
(ii) Non-Probability sampling [5 Marks]
(b) A sample survey of 5 families was taken and the figures obtained with respect to their
annual earnings 1 x ( in US$100’s), annual income 2 x ( in US$ 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 16 3
2 5 13 6
4 4 10 5
5 8 13 3
5
(a) Find the least – square multiple regression equations of 1 x on 2 x and 3 x
[7 Marks]
(b) Estimate the annual savings of a family whose size is 4 and annual income is
US$16,000. [3 Marks]
QUESTION FIVE
(a) (i) Define the term Expected monetary Value (EMV) [2 Marks]
(ii) List the three steps involved in calculating (EMV) [3 Marks]
b) A retailer purchases tomatoes every morning at $50 a case and sells them for $80 a
case. Any case remaining unsold at the end of the day can be disposed of the next day at a
salvage value of $20 per case thereafter they have no value. Past sales have ranged from 5
to cases per day. The following is the record of sales for the past 120 days
Cases sold 15 16 17 18
Number of days 12 24 48 36
(i) Construct a pay off table for the above problem [7 Marks]
(ii) Calculate the Expected Monetary Value (EMV) [6 Marks]
(iii) Find how many cases the retailer should purchase per day to maximize
profits [2 Marks]
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