**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]