**UNIVERSITY EXAMINATIONS: 2018/2019**

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

**INFORMATION TECHNOLOGY**

**BUSS305 STATISTICAL DECISION MAKING**

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

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

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

**QUESTION ONE (30 MARKS)**

(a)Define the following terms as applied in statistics

(i) Sampling distribution

(ii) Type I error

(iii) Ordinary Least Squares method

(iv) Parameter

(v) Critical region (5 Marks)

(b) In a study of malaria patients in Kisumu, it was established that persons who died from this disease

during each of the past ten years were as follows. 450,200,180,90,72,560,720,450,500 and 70. Calculate

the mean and 95% confidence interval for the data. (6 Marks)

(c) Briefly describe(i) stratified random sampling method.

(ii) Multistage sampling method (6 Marks)

(d) The manager of a supermarket recorded the number of customers who were served at the store

between 6.00pm and 9.00pm for 12 consecutive Thursdays. The results were as follows:

285 292 243 286 301 258 286 208 215 263 252 224

Find the (i) mean (2Marks)

(ii) Median (2Marks)

(iii) Standard deviation (3 Marks)

(e) It is claimed that the mean weight of students at KCAU is at least 62kgs with a standard deviation of

12kgs.To test this claim a random sample of 100students was taken and a sample mean weight of 56kgs

was obtained. Does this provide sufficient evidence to reject the claim at 5% level of significance?

(6 Marks)

**QUESTION TWO (20 MARKS)**

(a) Briefly describe three non-parametric tests commonly used in business. (6 Marks)

(b) A movie producer is bringing out a new movie. In order to map out his advertising campaign, he

wants to determine whether the movie will appear most to particular age group or it will appear

most to a particular age group or it will appear equally to all age groups. The producer takes a

random sample from persons at from persons attending a preview of the new movie and obtained

the following results.

At 5% level of significance, what inference will draw from this data?

(14 Marks)

**QUESTION THREE (20 MARKS)**

(a) Distinguish between one sided and two sided tests in hypothesis. (4 Marks)

(b) The weights of 18 cans of tinned fruits were obtained to test the claim that the mean weight is

17gms.The sample weights were obtained as follows:

12 20 13 10 18 26

30 19 22 15 14 11

20 21 23 17 18 24

Determine whether there is enough evidence to refute the claim at 5% level of significance.

(8 Marks)

(c) A university random sample of 120 male students and 80 female students has been taken. Among the

male students 37% say that computing facilities are not adequate, whereas 32% female students say

computing facilities are not adequate.

(i) Construct a 95% confidence interval for the difference between male and female

students’ opinion about computing facilities. (6 Marks)

(ii) At 95% level of confidence, is there is a significant difference between male and

female students opinion about computing facilities at the university? (2 Marks)

**QUESTION FOUR (20 MARKS)**

(a) Explain any three applications of regression analysis in business today. (6 Marks)

(b) In a random experiment to predict a person’s weight using the size of his shoe, the following data

was obtained.

(i) Draw a scatter diagram

(ii) Fit a regression line of Y on X

(iii) Predict the weight of a person who’s shoe is 9.0 inches.

(iv) Calculate the correlation coefficient. (14 Marks)

**QUESTION FIVE (20MARKS)**

(a) Give five reasons on why sampling may be preferred over complete enumeration

(census). (5 Marks)

(b) Explain the importance of statistics in Management Decision Making. (8 Marks)

(c ) 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? (2 Marks)

(ii) Which criteria is selected by the minim ax regret criterion? (5 Marks)