**MAASAI MARA UNIVERSITY**

**REGULAR UNIVERSITY EXAMINATIONS**

**2018/2019 ACADEMIC YEAR**

**FIRST YEAR FIRST SEMESTER**

**SCHOOL OF BUSINESS AND ECONOMICS**

**BACHELOR OF AGRIBUSINESS MANAGEMENT**

**COURSE CODE: AGB 2106**

**COURSE TITLE: BUSINESS STATISTICS**

**DATE: 5TH DECEMBER 2018 TIME: 11.00 -1.00PM**

**INSTRUCTIONS TO CANDIDATES**

**Answer Question ONE and any other THREE questions**

**This paper consists of 3 printed pages. Please turn over.**

**AGB 2106: Business Statistics Page 2**

**1. QUESTION ONE (25 MARKS)**

a) Explain the meaning of the word Population as applied to the study of statistics and

differentiate it from a sample. (3 marks)

b) Differentiate between each of the following as applied to statistics:

i. Parameter and statistic (2 marks)

ii. Descriptive statistics and inferential statistics (2 marks)

iii. Estimate and Estimator (2 marks)

iv. Point Estimate and interval Estimate (2 marks)

c) Given the data below

28 35 29 36 48 57 67 69 58 71

48 24 42 21 37 51 72 63 33 62

71 32 34 38 37 64 51 54 56 31

37 76 38 61 59 58 44 39 57 46

38 34 45 47 38 44 47 47 48 22

i. Develop a frequency distribution table of six classes (2 marks)

ii. Construct an ogive (2 marks)

d) Give three main reasons why the use of sample is more widely applied than that of

population in the study of statistics (3 marks

e) Give three qualities of a good Estimator (3 marks)

f) Differentiate between Chebyshevs rule and the Emperical rule as applied to the

understanding of the Standard deviation (4 marks)

**QUESTION TWO (15 MARKS)**

a) Explain the term probability as applied to statistics (2 marks)

b) Differentiate between each of the following as applied to the study of probability

i. Mutually exclusive and collectively exclusive events. (2 marks)

ii. Dependent and independent events (2 marks)

c) In a statistics class there are 100 students. In an exam taken at the end of academic year,

the scores they obtained were found to be normally distributed with a mean score of 50

marks and standard duration of 10 marks

Given that the university pass mark is 40, determine

i. The number of students who passed the exam (3 marks)

ii. The probability that at least a third of the students failed the exams (3 marks)

iii. The value of X if 20% of the students obtained a distinction by scoring a given mark

X and above. (3 marks)

AGB 2106: Business Statistics Page 3

**QUESTION THREE (15 MARKS)**

Sare industries has five production employees in total. The hourly earnings of each

employee is given as per the table below.

Required

a) Determine the population mean (2 marks)

b) Construct the sampling distribution of the means for sample of size 2 given

sampling is done without replenishment (6 marks)

c) Find the mean of the sample means (2 marks)

d) Find the number of samples if sampling is done with replenishment (2 marks)

e) Determine the standard error (3 marks)

**QUESTION FOUR (15 MARKS)**

a) Explain what is meant by the term correlation in statistics (2 marks)

b) A sample of 10 families in Nairobi revealed the following for family size and the amount

spent on food stuffs in Ksh.100, per month.

Required

i. Plot the information on a scatter diagram (3 marks)

ii. Compute the co-efficient of correlation (3 marks)

iii. Determine the coefficient of determination (1 marks)

iv. Determine the regression equation y on x (3 marks)

v. Determine the standard error of estimate (3 marks)

**QUESTION FIVE (15 MARKS)**

a) Give the steps necessary for the test of hypothesis (4 marks)

AGB 2106: Business Statistics Page 4

b) Using a flow chart differentiate between the use of a t-test and a z-test for the mean

(4marks)

c)A franchise investment company gives its average investment (in thousands) at Ksh.

143,260. You have some doubt and think this information is incorrect. You have decided to

randomly select 30 franchises and to help you determine the necessary investment for each.

Your sample mean investment is Ksh. 135,000 with a standard deviation of Ksh.30,000.

Determine if there is enough evidence to support your claim at α = 0.05

(7 marks)