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Cms 301-F Advance Business Statistics Question Paper
Cms 301-F Advance Business Statistics
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2011
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UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 301-F ADVANCE BUSINESS STATISTICS
DATE: DECEMBER2011 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any Other Two Questions
Question One
a) Define the terms simple random sampling and stratified random sampling (4 Marks)
b) A sample of size 16 is drawn, with replacement, from a normal distribution with mean of
1000 and standard deviation of 200. Find the following.
(i) P(800 < X < 1200)
(ii) (ii) P(X > 1050) (7 Marks)
c) Name and explain the four components of a time series (4 Marks)
d) Consider the following data concerning bond rate and prime interest rate
Bond rate % 5 12 9 15 7
Prime interest rate % 16 6 8 4 7
Find the regression equation of bond rates on prime interest rate (7 Marks)
e) Define the term coefficient of determination (2 Marks)
f) A manufacturing facility produces bearings. The diameter specified for the bearings is 5
millimeters. Every 10 minutes, six bearings are sampled and their diameters are measured
and recorded. Twenty of these samples are gathered and the following ranges were
tabulated.
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0.25, 0.12, 0.34, 0.10, 0.07, 0.05, 0.03, 0.09, 0.14, 0.18, 0.22, 0.11, 0.16, 0.21, 0.06, 0.12, 0.12,
0.09, 0.17, 0.09. Construct R-chart for the data. (6 Marks)
Question Two
a) (i) Describe the importance of time series analysis in business forecasting (2 Marks)
(ii) The amount of time the university professors devote to their jobs per week is normally
distributed with a mean of 52 hours and a standard de of 6 hours.
a. What is the probability that a professor works for more than 60 hours per week.
b. Find the probability that the mean amount of work per week for thee randomly
selected, without replacement, professors is between 50 hours and 60 hours. (10 Marks)
b) Kembo Holdings has seven accounts employees (considered population). The monthly
earnings (thousands shillings) of each employee are given below:
Employee Monthly Earnings(thousand Kes)
Randa 6
Temu 7
Karanja 8
Limo 9
Hassan 7
Lelgo 5
Mutua 6
Required:
(i) Compute the monthly mean earnings and standard deviation of the earnings
(ii) Form samples of size 2 without replacement,
(iii) What is the mean and standard deviation of the sampling distribution?
(10Marks)
Question Three
(a) Consider production data
year ‘91 ‘92 ‘93 ‘94 ‘95 ‘96 ‘97 ‘98 ‘99 ‘00 ‘01 ‘02
Sales.(000) 50 65 70 65 50 62 70 68 65 64 60 68
Calculate
(i) a 5- moving average
(ii) smoothing values by taking a = 0.1 (12 Marks)
(iii) Consider the following data.
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Year (X) Sales
(‘000) (Y)
2001 32
2002 47
2003 65
2004 92
2005 132
2006 190
2007 275
(b) Find the trend by using the equation Y = abX and estimate the sales in 2008
(8 Marks)
Question Four
(a) The table below presents the payoffs (returns) associated with five alternative types of
investment decisions for a 1-year period. Given that the probabilities associated with
the possibilities states are available,
(i) Determine the recommended decision under the standpoint of maximin and
maximax criterion ignoring the probabilities ( 8 Marks)
(ii) Determine the recommended decision under the standard point of the
bayesian criterion of maximizing the expected payoff ( 8 Marks)
State of
econony
Probability A1
Savings
Acc
A2
Corp
bonds
A3
Blue
chips
A4
Spec.
stocks
A5
Stock
options
E1:
Recession
E2: Stable
E3:
0.3
0.5
0.2
600
600
600
500
900
900
-2,500
800
4,000
-5,000
400
10,000
-10,000
-5,000
20,000
4
Expansion
(b) The data shows the number of chips per bag for five samples of seven bags of chips.
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
25 22 30 32 25
23 21 23 26 23
29 24 22 27 29
31 25 26 28 27
26 23 28 25 27
28 26 27 25 26
27 29 21 31 24
Construct X chart and an R chart (12 Marks)
Question Five
(a) The table below shows the corresponding values of three variables, X1 = cost of
advertisement, X2 = salary of salespersons and X3 = sales of a product
X1 4 6 7 9 13 15
X2 15 12 8 6 4 3
X3 30 24 20 14 10 4
(i) Find the least-squares regression equation of X1 on X2 and X3
(ii) Compute the coefficient of multiple correlation, R1,.23
(iii)Estimate the value of X1 when X2 = 10 and X3= 12 (12 Marks)
(b) Consider the following probability distribution
x 1 2 3 4 5 6
p(x) 1/6 1/6 1/6 1/6 1/6 1/6
(i) Find the distribution of the population
(ii) Form samples of size 2 and find the distribution of the mean of the samples.
(8 Marks)
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