UNIVERSITY EXAMINATIONS: 2016/2017
EXAMINATION FOR THE DEGREE OF BACHELOR OF BUSINESS
INFORMATION TECHNOLOGY
BUSS 305 STATISTICAL DECISION MAKING
DISTANCE LEARNING
DATE: AUGUST, 2017 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.
QUESTION ONE [30 MARKS]
a) Define the following
i. Type I error [2 Marks]
ii. Type II error [2 Marks]
b) In a company MachineYproduces40compact disks whose mean diameter is15 cmwith standard deviation0.5.Machine
Zproduces60compact disks whose meandiameter was15.6 cmwith standard deviation0.8. At5%level of significance, test
whether there is a difference between the two machines. [6 Marks]
c) A manufacturer claims that its new car gives mileage of at least
10
kilometre per litre
(km.p.l) of petrol. A sample of
10
cars is taken and their mileage recorded as follows (in
km.p.l).
10.2, 10.7 ,11.3 ,11.0 ,10.8 ,10.7 ,10.6 ,10.6 ,10.7 ,10.4
Is there any statistical evidence to support the claim of the manufacturer about the
mileage of its car? Test at
95%
level of confidence.
[7 Marks]
d) A total of 1,600 families were selected at random in a city to test the belief that high
income families usually send their children to private schools and low income families
often send their children to government schools. The following results were obtained.
Test whether income and type of schooling are independent. Test at 5% level of
significance.
[8 Marks]
e) A sample of 400 items is taken from a population whose standard deviation is 15. The
mean of the sample is 25.Test whether the sample has come from the population with
mean 26.8. Also calculate the 98% confidence limits of the population mean.
[5 Marks]
QUESTION TWO [20 MARKS]
a) State and explain the four qualities of a good estimator.
[8 Marks]
b) In a sample of 600 men from a certain city, 450 men are found to be smokers. In a
sample of 900 from another city 450 are found to be smokers. Do the data indicate that
the two cities are significantly different with respect to prevalence of smoking habit
among men? Test at 5% significance level.
[6 Marks]
c) To test the intelligence of 10th class boys and girls in a Higher secondary school, a sample
of 83 tenth class boys and a sample of 95 tenth class girls were taken and intelligence
tests applied. The following results were observed:
Is there a significant difference in the mean scores obtained by boys and girls? Test at
5% significance level. [6 Marks]
QUESTION THREE [20 MARKS]
a) State the four principal component of a time series. [4 Marks]
b) Explain the difference between multiplicative and additive models as used in time series
stating the conditions under which each is used. [4 Marks]
c) List two uses of the seasonal index. [2 Marks]
d) The table below shows the sales of new cars by quarters during a period of three years.
Assuming the additive model, determine the seasonal index for each quarter.
[10 Marks]
QUESTION FOUR [20 MARKS]
a) Memory capacity of
9
students was tested before and after training. State whether
training was effective or not from the following scores: Use
[6 Marks]
b) The lifetime of a certain type of a computer component manufactured by a certain factory
are normally distributed with mean of
800
hours and standard deviation of
160
hours.
i. The manufacturer replaces all components that fail before the guaranteed
minimum lifetime of
600
hours. Determine the percentage of the
components that have to be replaced. [3 Marks]
ii. Determine the guarantee lifetime if the manufacturer only wished to
replace
1% of the components. [4 Marks]
iii. Determine the probability that the mean lifetime of a sample of
25
of
these computer exceeds
850
hours. [3 Marks]
c) Explain four qualities of a good estimator. [4 Marks]
QUESTION FIVE [20MARKS]
a) State two advantages and two disadvantages of stratified sampling. [4 Marks]
b) Differentiate between Bayes’ and maximax rules. [4 Marks]
c) A computer firm is considering venturing into personal computer market with a new design.
They have developed prior probabilities and the expected five year’s profit figures as
follows:
If they decide not to enter the market, they can sell their patents for the product for one million
shillings. Another alternative open to them is to hire a market survey company to conduct an
analysis of potential sales. This would cost Ksh 0.25 million and the outcome of the survey
would either be favorable or unfavourable.Baesd on past experience the probability for various
options is as follows:
( ) 0.39
( ) 0.61
( / ) 0.5574
(mod / ) 0.5082
( / ) 0.344
( / ) 0.4426
(mod / ) 0.4918
( / ) 0.656
probability unfavoarble
probability favorable
probability highsales unfavorable
probability eratesales unfavorable
probability low sales unfavorable
probability highsales favorable
probability eratesales favourable
probility low sales favorable
Using a decision tree, determine the best decision for the firm. [12 Marks]
