**UNIVERSITY EXAMINATIONS: 2017/2018**

**EXAMINATION FOR THE DEGREE OF BACHELOR OF BUSINESS IN **

**INFORMATION TECHNOLOGY**

**BUSS 305 STATISTICAL DECISION MAKING**

**FULL TIME/PART TIME/DISTANCE LEARNING**

**DATE: AUGUST, 2018 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.**

**QUESTION ONE (30 MARKS)**

(a) Differentiate between

i. A sample and a Population

ii. Systematic sampling and stratified sampling

iii. Null hypothesis and alternative hypothesis

iv. Type I error and Type II error [8 Marks]

(b) List THREE advantages of simulation [3 Marks]

(c) According to recent information from the Kenya Automobile Association, the mean age of

passenger cars in Kenya is 8.4 years. A sample of 40 cars in the student’s lot at KCA showed

the mean age to be 9.2 years. The standard deviation of this sample was 2.8 years. At the

0.01 significance level can we conclude the mean age is more than 8.4 years for these cars of

KCA students?

i. State the null hypothesis and the alternative hypotheses.

ii. Explain why z is the test Statistic

iii. What is the critical value of the test statistic?

iv. Compute the value of the test statistic

v. What is your decision regarding the null hypothesis? Interpret your decision.

[8 Marks]

(d) A sociologist was hired by a large hospital to investigate the relationship between the

numbers of unauthorized days that an employee is absent per year and the distance between

home and work for that employee. A sample of ten employees was chosen and the following

data was collected.

Distance to work (X) 1 3 5 6 8 10 12 14 16 18

Days absent (Y) 3 8 9 7 6 6 5 4 3 2

i. Draw a scatter diagram to illustrate this information. [4 Marks]

ii. Calculate the coefficient of correlation and interpret your results. [4 Marks]

iii. Compute the coefficient of determination and interpret it. [3 Marks]

**QUESTION TWO (20 MARKS)**

(a) Define the following terms as used in statistics

i. Critical region

ii. Confidence interval

iii. Statistical Inference [6 Marks]

(b) The performance in two subjects by a sample of BBM students were as follows

Statistics 40 82 59 87 33

Quantitative Methods 35 30 56 45 42 37

i. Compute the mean and standard deviation of Statistics scores [5 Marks]

ii. Calculate the mean and the standard deviation of quantitative methods scores [5 Marks]

(c) Determine if there is a significant difference between the mean score of the two subjects

given that α = 5% Determine the minimum required sample size if you want to be 99%

confident that the sample mean is within two units of the population mean, given that 𝜎 =

1.4. Assume that the population is normally distributed. [4 Marks]

**QUESTION THREE (20 MARKS)**

(a) Discuss the significance of hypothesis testing in business. [6 Marks]

(b) Give three areas when chi-square test can be applied. [6 Marks]

(c) The following data represent a survey that was recently conducted on different resort island

in which luxury enterprises has three different hotels.

Find whether there is a significance difference of the guest likely to return to the hotel again

between the three hotels, at 5% significance level. [8 Marks]

**QUESTION FOUR (20 MARKS)**

(a) Differentiate between correlation and regression [5 Marks]

(b) A manufacturer would like to develop a method of estimating direct labour cost for small

batch production orders. He has obtained a random sample of actual direct labour cost which

has been recorded for ten batches as follows:

i. Plot a scatter diagram to represent this information [4 Marks]

ii. Compute the Pearson Product Moment Correlation Coefficient, hence interpret

your results. [5 Marks]

iii. Determine the equation of the linear regression of 𝑦 on 𝑥 and interpret the

coefficient. [6 Marks]

**QUESTION FIVE (20 MARKS)**

(a) Explain the importance of statistics in Management Decision Making. [8 Marks]

(b) . An investor is considering three alternatives-a certificate of deposit, a low risk stock fund, and

a high risk stock fund- for a $20,000 investment. The investor considers three possible states of

nature

(i) Which action is selected by the investor if he is a risk seeker? [2Marks]

(ii) Which action is selected by the investor if he is a risk averter? [2Marks]

(iii) Which criteria is selected by the minim ax regret criterion? [5Marks]

(iv) Draw the decision tree for the investor’s problem. [3Marks]