Business Statistics Question Paper

Business Statistics

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2010

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
OPEN, DISTANCE AND E-LEARNING EXAMINATION FOR THE DEGREE
OF BACHELOR OF COMMERCE
BMS 200: BUSINESS STATISTICS

DATE: Friday 23rd July, 2010
TIME: 2.00 p.m. – 4.00 p.m.
________________________________________________________________________

INSTRUCTIONS
Answer question ONE and any TWO questions.

QUESTION ONE (COMPULSORY – 30 MARKS)
a)
Assume that family incomes are normally distributed with µ = 16000 dollars
s=2000 dollars. What is the probability that a family picked at random will have
an income
i)
Between 15000 dollars and 18000 dollars?

[3 marks]
ii)
Below 15000 dollars?

[2 marks]
iii)
Above 20000 dollars?

[2 marks]
b)
Suppose that a prospective buyer tests bursting pressure of samples of polythene
bags received from two manufacturers A and B. The test reveals the following
results:

Bursting pressure (lbs) 5 - 10
10 - 15
15 - 20
20 - 25
25 - 30
Number of bags (A)
2
9
29
54
6
Number of bags (B)
9
15
30
32
14

i)
Calculate the mean number of bags for both manufacturer A and B.

[3 marks]
Page 1 of 6

ii)
Calculate the standard deviation for each manufacturer.
[4 marks]

iii)
Calculate the coefficient of variation for each manufacturer.

[2 marks]
iv)
Which manufacturer’s bags, judging from the two samples, have the
higher average bursting pressure? Which of them is more uniform in
bursting pressure?

[2 marks]
c)
For 10 observations on price (X) and supply (Y), the following data were
obtained.

?
X ?

130,

?Y ?

,
220
X2
? ?

2288,

Y2
? ?

5506,

?

XY ? 3467

i)
Fit a linear regression of Y on X.

[5 marks]

ii)
Estimate supply when the price is 25 units.

[1 mark]

d)
Briefly explain the four components of a time series.

[4 marks]
e)
Distinguish between estimation and hypothesis testing.

[2 marks]

QUESTION TWO (20 MARKS)
a)
i)
Find the spearman rank correlation coefficient between the mid-term
grade and the IQ ranking of a random sample of 10 students in a large
class as given in the table below. The data below relates the weekly
maintenance cost (£) to the age (in months) of ten machines of similar
type in a manufacturing company
Student
1
2
3
4
5
6
7
8
9
10
Mid-term grade
77 78 65 84 84 88 67 92 68 96
IQ ranking
7

[5 marks]

ii)
When is the rank correlation used?

[2 marks]
b)
Given below is time series data for 12 years – 1989 to 2000 relating to sales of a
certain business firm.
Year
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Sales(million
10
15
20
25
15
12
15
24
15
21
15
24
Ksh)

Calculate a three-year moving averages, starting from 1989.
[7 marks]

Page 2 of 6

c)
Given the following weights of five persons in lbs: 120, 140, 150, 160, 180, find

i)
Mean

[2 marks]

ii)
Variance

[3 marks]

iii)
Standard deviation

[1 mark]

QUESTION THREE (20 MARKS)
a)
Define type I and type II errors.

[2 marks]
b)
An army recruiting center knows from experience that the weight of army recruits
is normally distributed with a mean µ of 80kg and a standard deviation s of 10kg.
The recruiting center wants to test, at 1% level of significance, if the average
weight of this year’s recruits is above 80kg. To accomplish this, it takes a random
sample of 25 recruits and finds that the average weight for this sample is 85kg.

i)
Formulate the null and alternative hypotheses for this test. [2 marks]

ii)
Test whether the average weight of this year’s recruits is above 80kg.

[6 marks]

c)
From the following data construct an index number for 2005 taking 2004 as base:

Commodity and unit
Price (dollars)
Price (dollars)

2004
2005
Butter (1kg)
110.0
120.00
Cheese (1kg)
75.00
80.00
Milk (1 litre)
13.00
13.00
Bread (1)
9.00
9.00
Eggs (dozen)
18.00
20.00
Ghee (1 tin)
850.00
860.00

d)
A random sample of 200 consumer accounts at a large brokerage firm is selected
for the purpose of estimating the mean number of transactions per year for each
customer. The sample mean is found to be 43 and sample standard deviation is
2.5. Determine 99% confidence interval for the mean number of transactions of
all consumer accounts of the firm.

[6 marks]

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