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Business Statistics Ii Question Paper
Business Statistics Ii
Course:Bachelor Of Commerce(Bcom) ()
Institution: Kabarak University question papers
Exam Year:2009
KABARAK
UNIVERSITY
UNIVERSITY EXAMINATIONS
2009/2010 ACADEMIC YEAR
FOR THE DEGREE OF BACHELOR OF COMMERCE
COURSE CODE: BMGT 220
COURSE TITLE: BUSINESS STATISTICS II
STREAM:
Y2S2
DAY:
THURSDAY
TIME:
9:00 A.M.– 11:00A.M.
DATE:
10/12/2009
Instructions
Answer question ONE and any other TWO questions.
Page 1 of Page 4
1. (a) Explain the following distributions and explain the application of each
(i) t-distribution
(5mks)
(ii) Chi-square distribution
(5mks)
(b) (i) Distinguish between a mathematical model and a statistical model
(3mks)
(ii) Explain Literature Review and give its importance in statistical research.
(3mks)
(c) (i) Distinguish between Permutation and Combination
(4mks)
(ii) A consumer is requested to rank in order of preference the taste of five brands.
If she is indifferent among these brands, what is the probability that an
individual who is truly indifferent will select a specific ordering for the first
three places?
(3mks)
(d) Given letters ABC, show in how many ways these letters can be permutated using a
tree diagram.
(2mks)
(e) (i) What is an expected value
(2mks)
(ii) In a given business venture, a person is able to make a gain of Kshs. 300 with a
probability of 0.6 or take a loss of Kshs. 100 . What is the persons expected
value if he/she gets involved in the venture?
(3mks)
2. (a) Suppose Kabarak University has bought 4000 bulbs. The lifetime of the bulbs has
historically been realized to be normally distributed with mean of 700 hours and a
standard deviation of 130 hours. How many bulbs are expected to fail in the first
550 hours.
(5mks)
(b) Explain the following probability distributions
(i) Binomial distribution
(3mks)
(ii) Sampling distribution of the mean
(3mks)
(c) Given the following information on sales of cars by a given saleslady per day:
No. of cars sold
Probability
0
0.10
1
0.15
2
0.30
3
0.30
4
0.15
(i) What kind of distribution is this? Give reasons
(3mks)
(ii) How many cars does this saleslady sell on a typical day?
(3mks)
(iii) What is the variance of the sales?
(3mks)
Page 2 of Page 4
3. (a) Mr. X, a salesman in industrial chemicals, has sales of Kshs. 200,000. The industrial
chemical department had mean sales of Kshs. 120,000 and a standard deviation of
Kshs. 40,000. On the other hand, Kamau, a sales person in office supplies department
had mean sales of Kshs. 100,000. The office supplies department had sales of Kshs.
40,000 and a standard deviation of Kshs. 20,000. Compare their performance.
(5mks)
b) (i) What are the desirable properties of confidence intervals?
(3mks)
(ii) A random sample of 16 observations from a normal population with standard
deviation of 6 had a mean of 25. Find a 90 percent confidence interval for the
population mean.
(5mks)
c) A researcher wishes to determine whether salaries of clerks employed by the private
sector are higher than those employed by the government. She collects a sample of
clerks from each sector and calculates the means and standard deviations of their
salaries as:
Private
Government
X 1 = 36,800
X = 35,400
2
S1 = 600
S2 = 450
n1 = 10
n2 = 8
At 1% level, can she conclude that the private sector pays more than the
government?
(7mks)
4. (a) Explain the classical assumptions of the least squares estimators (6mks)
(b) Given the following data on consumption expenditure and monthly earnings;
Consumption Expenditure Kshs. ‘000’
Disposable Income Kshs. ‘000’
5
5
6
7
13
10
10
15
17
20
22
25
15
25
20
30
25
30
i) Develop a graphical plot of the data and explain the nature of the relationship.
(4mks)
ii) Compute the least squares regression line for the variables.
(7mks)
iii) Interpret the economic meaning of the estimates
(3mks)
5. (a) (i) What is degrees of freedom?
(2mks)
(ii) A random variable is distributed about a mean µ with a variance of 96. A
random sample of 16 observations taken in the past gives a sample variance of 104.
Is this outcome attributable to chance or can it be taken as evidence that variability
of the population, as measured by 2
d , has risen?
(5mks)
Page 3 of Page 4
b) Cash and Carry supermarkets sales director intends to establish if there are any
significant differences between regions in terms of the degree of acceptance of a
new product. Using a sample and questionnaire technique, he obtained the following
data:
Region
Degree of acceptance
East
West
Poor
21
36
Moderate
83
56
Strong
24
17
i) Determine the expected sample results.
(3mks)
ii) Calculate the Chi – square statistic
(4mks)
iii) Establish the degrees of freedom.
(3mks)
iv) Test the null hypothesis that the degree of acceptance does not differ from
region to region at 5 percent significance level.
(3mks)
Page 4 of Page 4
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