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Introduction To Business Statistics Question Paper
Introduction To Business Statistics
Course:Bachelor Of Commerce
Institution: Kenyatta University question papers
Exam Year:2009
UNIVERSITY EXAMINATIONS: 2009/2010
SECOND YEAR
INTRODUCTION TO BUSINESS STATISTICS
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer ONE and Any other TWO Questions
QUESTION ONE
a) Differentiate between the following terminologies as applied in business statistics
i) Type I and type II error [2 Marks]
ii) Statistics and a statistic [2 Marks]
b) An analysis of weekly wages paid to workers in two firms A and B belonging to the same
industry gives the following results:
Firm A Firm B
Number of wage-earners 550 650
Average daily wages 50 45
Variance of the distribution wages 90 120
(i) Which firm pays out a larger amount as daily wages? [5 Marks]
(ii) In which firm is there greater variability in individual wages? [2 Marks]
c) In preparation for an appropriate hearing the DCP of a city Zone has collected the following
information
2
Type of crime 2000 2001 Weight
Robberies 13 8 6
Car thefts 15 22 5
cycle theft 149 185 4
Pick pocketing 328 259 1
Theft of servants 479 488 2
Calculate the index of crime from 2001 using 2000 as the base year
[6 Marks]
d) Suppose an item is manufactured by three machines X, Y and Z. all the machines have equal
capacity and are operated at the same rate. It is known that the percentage of defective items
produced by X, Y and Z. are 2, 7 and 12 percent respectively. All the items produced by X, Y and
Z. are put into one bin. From the bin one item is drawn at random and it is found to be defective.
Find the probability that this item was produced on machine Y.
[6 Marks]
e) Determine regression equation of y on x from the following data
X 1 2 3 4 5
Y 2 5 3 8 7
[7 Marks]
QUESTION TWO
a) The following table gives the classifications of 100 workers according to sex and the nature of
work. Test whether nature of work is independent of the sex of the worker. [5 Marks]
Skilled Unskilled
Males 40 20
Females 10 30
3
b) The table below gives the weight measurements of 200 castings
Calculate:
i) Arithmetic Mean using an assumed mean weight of 125.5 Kgs. [3 Marks]
ii) Median [3 Marks]
iii) Mode [4 Marks]
iv) Standard deviation [5 Marks]
QUESTION THREE
a) The following data relate to the number of passenger cars (in million) sold by ABC company from
2000-2007
i) fit a straight trend line to the data
through 2005 only
[8 Marks]
ii) Use your result in (i) to estimate
production in 2008.
[2 Marks]
Weight
(Kgs)
No. of
Castings
Weight
(Kgs)
No. of
Castings
81-90 2 141-150 37
91-100 5 151-160 29
101-110 13 161-170 11
111-120 20 171-180 3
121-130 30 181-190 1
131-140 49
Year Number Year Number
2000 6.7 2004 5.6
2001 5.3 2005 7.9
2002 4.3 2006 5.8
2003 6.1 2007 6.1
4
b) A food processor uses a moving average to forecast next month’s demand. Past actual demand (in
units) is shown below:
Month 43 44 45 46 47 48 49 50 51
Actual
demand
105 106 110 110 114 121 130 128 137
i) Compute a simple five moth moving average to forecast demand for month 52
[6 Marks]
ii) Compute a weighted three month moving average where the weights are highest for the
latest month and descend in order 3, 2 and 1 [4 Marks]
QUESTION FOUR
a) Define the term Expected Monetary Value (EMV). [2 Marks]
b) Explain the four steps in decision making process as applied in Decision Theory
[4 Marks]
c) A retailer purchases ripe tomatoes every morning at Kshs 500 a case and sells them for Kshs 800 a
case. Any case remaining unsold at the end of the day can be disposed of at the end of the day at a
salvage value of Kshs 200 per case. Thereafter, they have no value. Past sales have ranged from 15
to 18 cases per day. The following is the record of sales for past 120 days:
Find how many cases the retailer should purchase per day to maximize his profits.
[8 Marks]
d) Two sales men A and B working for the same company have recorded their sales over a period of
time. The mean sales and standard deviation for the sales are given in the following table
Cases sold 15 16 17 18
Number of days 12 24 48 36
A B
5
Is there a significant difference between sales of the two sales men? Test at 95% level of
significance [6 Marks]
QUESTION FIVE
a) Differentiate between regression and correlation analysis. [2 Marks]
b) The following data relate to age of employees and the number of days they were reported sick
in a month:
Employees 1 2 3 4 5 6 7 8 9 10
Age (X) 30 32 35 40 48 50 52 55 57 61
Sick days (Y) 1 0 2 5 2 4 6 5 7 8
Calculate the Karl Pearson’s correlation coefficient and interpret the results [8 Marks]
c) Differentiate between Paasche and Laspeyre index numbers [2 Marks]
d) The following data relate to price and quantity of items for 2007 and 2008.
Commodities
2007 2008
Price Quantity Price Quantity
A 2 8 4 6
B 5 10 6 5
C 4 14 5 10
D 2 19 2 13
Construct index numbers for price using:
i) Laspeyre method [3 Marks]
ii) Paasche method [3 Marks]
Number of days of sales 20 18
Average sales per day 170 205
Standard deviation 20 25
6
iii) Fisher’s ideal method [2 Marks]
iv) Bowley’s method [2 Marks]
c) The following table gives the classifications of 100 workers according to sex and the nature of
work. Test whether nature of work is independent of the sex of the worker. [5 Marks]
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