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Advanced Statistics Question Paper

Advanced Statistics

Course:Bachelor Of Commerce

Institution: Kca University question papers

Exam Year:2010

UNIVERSITY EXAMINATIONS: 2009/2010
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
CMS 301: ADVANCED STATISTICS (SUNDAY)
DATE: AUGUST 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) (i) Define time series (1 Mark)
(ii) State any two causes of forecast errors in trend values of a time series. (2 Marks)
(iii) In time series analysis, under what circumstances would the multiplicative model be preferred
to the additive model? (2 Marks)
b) Demand for some spare part is given below.
Month April 2008 May 2008 June 2008
Demand 200 50 150
The forecast for April 2008 was 100 units.
Determine the demand for July 2008 taking a=0 (6 Marks)
c) Out of 300 house holds in a large town,123 have colour TV. Give 95% confidence limit, of the true
value of proportion of households in the whole town with colour TV. (4 Marks)
d) A drug company conducts a test comparing a new experimental insecticide with their standard
brand. Under controlled conditions the standard brand kills 475 out of 600 mosquitoes in one
minute, while the experimental spray kills 509 out of 600 mosquitoes in the same time. Does this
suggest that the experimental insecticide is significantly more effective than the standard brand at
5% level of significance? (6 Marks)
2
e) The table below shows the possible net returns(discounted to present)and associated probabilities
of two investments to be undertaken by a particular company.
Net returns(sh
000)
-3 -2 -1 0 1 2 3 4
Probability:
Investment 1
0 0 0.1 0.2 0.3 0.2 0.2 0
Probability:
Investment 2
0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2
Determine the best investment option for the company. (4 Marks)
f) In a particular dairy farm, milk production from the population of animals was found to
occasionally vary due to weather changes. A periodic check is done on the milk production to
ensure that the mean and standard deviation are 50 litres and 2.5 litres respectively. In a particular
day a sample of 12 animals produced the following quantities of milk (in litres)
43 51 50 41 53 52 47 54 51 45 48 47
If the production manager will welcome any change of the population mean towards higher values
but safeguard against decreasing values:
(i) Formulate the null and alternative hypothesis for this situation;
(ii) Using a=0.05, test the hypothesis. (5 Marks)
QUESTION TWO
(a) In estimation, a statistic is used to estimate a parameter. Distinguish between the two and discuss
two ways in which a parameter may be estimated using a statistic. (8 Marks)
(b) A random sample of 40 computer staff had their heights cm, recorded. The results were as
summarized below:
SX=7815 SX2=1,537,927
Assuming that the heights are normally distributed:
i. Test at 5% confidence level whether the mean µ, of the heights is less than 200cm.
ii. Determine the 95% confidence interval for the mean µ. (12 Marks)
3
QUESTION THREE
(a) (i) Define the four fundamental characteristics of a time series (4 Marks)
(ii)State any THREE factors that make a time series analysis an important tool in business decision
making. (3 Marks)
(b) The managers of a software company are preparing revenue plans for the last quarter of 2001/2002
and for the first three quarters of 2004\2005.The data in the table below refers to one of the main
product.
Revenue(£’000’)
Quarter
Year 1 2 3 4
2001/2002 49 37 58 67
2002/2003 50 38 59 68
2003/2004 51 40 60 70
2004/2005 50 42 61 -
(i) Calculate the four-quarterly moving average trend for this set of data. (2 Marks)
(ii) Assuming a multiplicative model, calculate the seasonal factors. (8 Marks)
(iii) Explain how you would use the results in part b(i)and b(ii) to forecast the revenue for
the last quarter of 2004/2005 and for the first three quarters of 2005/200 (3 Marks)
QUESTION FOUR
a) The following regression was calculated for a class of 24 BCOM students in KCAU
Y=3.1+0.021X1+0.075X2+0.043X3
Standard (0.019) (0.034) (0.018)
Error
Where Y= Students score on a theory examination
X1=Students rank (from the bottom) in high school
X2=Students verbal aptitude score
X3=A measure of the students character
(i) Calculate the t ratio and 95% confidence interval for the regression coefficient of X1 ( 4 Marks)
(ii) What assumptions did you make in (a) above. (2 Marks)
(iii) Is the regress X2 statistically significant (4 Marks)
4
b) The table below shows the number of defective plugs recorded by a statistical quality controller
working for a plug producing factory.
Lot Number Number of defective plugs Number of plugs in the lot
1 4 100
2 11 110
3 9 105
4 8 97
5 6 98
Construct an appropriate chart for the data and comment on the production process. (10 Marks)
QUESTION FIVE
(a) Kensafa Company Ltd is considering introducing two new products in the market. The company
can either introduce none, or just one of the two products or both of them. The success of these
products depends on the consumer’s reaction to the products. The reactions can be summarized as”
good” having probability (Pr(g)=0.3,”fair”having probability Pr(f)=0.6 and “poor” having
probability Pr(p)=0.1.The company’s revenues in millions of shillings are estimated as shown in
the table below.
Decision State of nature
g f p
None 0 0 0
Both 220 110 40
Product I only 125 65 30
Product II only 105 60 30
(i) Compute the expected monetary value for each decision. (4 Marks)
(ii) What decision would you recommend under the expected monetary criterion? (1 Mark)
(iii)Develop an opportunity loss table (4 Marks)
(iv) Compute the expected value of perfect information. (3 Marks)
(b) George, a business man, would like to borrow shs 300,000 from a bank in order to finance a
project. The money is to be repaid within one year. The bank charges a 15% p.a simple interest.
The bank may grant the loan or invest the same amount and be guaranteed a return of 9% p.a.From
past experience at the bank,4% of clients granted loans default on repayment.
(i) Using this information, construct a pay-off table for the bank. (4 Marks)
(ii) Draw a decision tree to represent this information. (3 Marks)
(iii) Determine the decision for the bank (1 Mark)

Advanced Statistics Question Paper

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