BUSINESS
STATISTICS COURSE OUTLINE
PRE –REQUISITE: - BBM 112, BBM 212 and BBM 223.
PURPOSE: - To equip students with data collections skills, correlations, analysis hypothesis
formulation and testing methods
OBJECTIVES: - By the end of this module, the learner should be able to: -
(a) Compute the correlation coefficient, equation of the regression line and the coefficient of
determination.
(b) Test the hypothesis Ho : P = 0
(c) Draw the scatter plots and correlation.
(d) Test the difference between two variances or standard deviations.
(e) Test the difference between sample means, and between two proportions using the z –
test.
(f) State the null and alternative hypothesis
(g) State the five steps used in hypothesis testing.
(h) Test means when is known using the z- test and chi-square.
(i) Test hypothesis, using the sign test, wilcoxon rank sum test and the Kruskal – Wallis test.
WEEK CONTENT
1 Measure of variation correlation, Pearson product moment coefficient r.
2 Regression analysis. Coefficient of determination. The rank correlation coefficient
1
, BUSINESS
3
STATISTICS
Sampling theory, types of sampling mean and standard deviation in simple
sampling attributes.
4 Large sample testing the significance for a single proportion.
5 Definition used in hypothesis testing, steps in hypothesis testing – traditional
method. Z-test for a mean.
6 Z – Test for a proportion chi-square testing. CAT 1 sit in.
7 Test of proportions. Test the difference between sample means using z-test; test the
difference between two means for independent samples, using the t-test.
8 Testing hypothesis about proportion hypothesis testing of the difference between
proportions. Testing the hypothesis for equity of two variances.
9 Advantages and disadvantages of non parametric methods. Test of hypothesis using
the Wilcoxon rank sum test.
10 Test hypothesis using the Kruskal Wallis test
11 Revision: using revision questions
12 Tutorials and revision consultations
13 Examination and consultation
14 Examination and consultation
Course evaluation:
Cat 1 seat in 1 hour examination from week one to six taking 15% of overall marks.
2
, BUSINESS
STATISTICS
Cat II distance cat to b handed in week 12 taking 15% of overall marks.
Final examination at the end of the semester 70% overall examination, any one of the
examinations not done will incomplete results
TABLE OF CONTENTS
COURSE OUTLINE ...................................................................................................................... 1
TABLE OF CONTENTS ............................................................................................................... 3
CHAPTER 1: CORRELATION AND REGRESSION ............................................................ 6
1.1 WHAT IS CORRELATION? ............................................................................................... 6
1.2 PEARSON’S PRODUCT MOMENT COEFFICIENT OF CORRELATION .................... 7
1.3 REGRESSION ANALYSIS ............................................................................................... 14
3
, BUSINESS
STATISTICS
1.4 COEFFICIENT OF DETERMINATION ........................................................................... 18
1.5 THE RANK CORRELATION COEFFICIENT (R) .......................................................... 20
1.6 TIED RANKINGS .............................................................................................................. 22
1.7 TIME SERIES ANALYSIS ................................................................................................ 24
CHAPTER TWO: SAMPLING THEORY .............................................................................. 30
2.1 SAMPLING: ....................................................................................................................... 31
2.2 TYPES OF SAMPLING ..................................................................................................... 31
2.3 MEAN AND STANDARD DEVIATION IN SIMPLE SAMPLING OF ATTRIBUTES 32
2.4 LARGE SAMPLES: TESTING THE SIGNIFICANCE FOR A SINGLE
PROPORTION ......................................................................................................................... 32
CHAPTER THREE: TEST OF HYPOTHESIS...................................................................... 35
3.1 INTRODUCTION:- ............................................................................................................ 36
3.2 TRADITIONAL METHOD ............................................................................................... 37
3.3 NULL AND ALTERNATIVE HYPOTHESIS .................................................................. 37
3.4 SIMPLE AND COMPOSITE HYPOTHESIS .................................................................... 37
3.5 TEST – STATISTIC ........................................................................................................... 38
3.6 ACCEPTANCE AND REJECTION REGIONS ................................................................ 38
3.7 TYPE I AND TYPE II ERRORS ...................................................................................... 38
4
STATISTICS COURSE OUTLINE
PRE –REQUISITE: - BBM 112, BBM 212 and BBM 223.
PURPOSE: - To equip students with data collections skills, correlations, analysis hypothesis
formulation and testing methods
OBJECTIVES: - By the end of this module, the learner should be able to: -
(a) Compute the correlation coefficient, equation of the regression line and the coefficient of
determination.
(b) Test the hypothesis Ho : P = 0
(c) Draw the scatter plots and correlation.
(d) Test the difference between two variances or standard deviations.
(e) Test the difference between sample means, and between two proportions using the z –
test.
(f) State the null and alternative hypothesis
(g) State the five steps used in hypothesis testing.
(h) Test means when is known using the z- test and chi-square.
(i) Test hypothesis, using the sign test, wilcoxon rank sum test and the Kruskal – Wallis test.
WEEK CONTENT
1 Measure of variation correlation, Pearson product moment coefficient r.
2 Regression analysis. Coefficient of determination. The rank correlation coefficient
1
, BUSINESS
3
STATISTICS
Sampling theory, types of sampling mean and standard deviation in simple
sampling attributes.
4 Large sample testing the significance for a single proportion.
5 Definition used in hypothesis testing, steps in hypothesis testing – traditional
method. Z-test for a mean.
6 Z – Test for a proportion chi-square testing. CAT 1 sit in.
7 Test of proportions. Test the difference between sample means using z-test; test the
difference between two means for independent samples, using the t-test.
8 Testing hypothesis about proportion hypothesis testing of the difference between
proportions. Testing the hypothesis for equity of two variances.
9 Advantages and disadvantages of non parametric methods. Test of hypothesis using
the Wilcoxon rank sum test.
10 Test hypothesis using the Kruskal Wallis test
11 Revision: using revision questions
12 Tutorials and revision consultations
13 Examination and consultation
14 Examination and consultation
Course evaluation:
Cat 1 seat in 1 hour examination from week one to six taking 15% of overall marks.
2
, BUSINESS
STATISTICS
Cat II distance cat to b handed in week 12 taking 15% of overall marks.
Final examination at the end of the semester 70% overall examination, any one of the
examinations not done will incomplete results
TABLE OF CONTENTS
COURSE OUTLINE ...................................................................................................................... 1
TABLE OF CONTENTS ............................................................................................................... 3
CHAPTER 1: CORRELATION AND REGRESSION ............................................................ 6
1.1 WHAT IS CORRELATION? ............................................................................................... 6
1.2 PEARSON’S PRODUCT MOMENT COEFFICIENT OF CORRELATION .................... 7
1.3 REGRESSION ANALYSIS ............................................................................................... 14
3
, BUSINESS
STATISTICS
1.4 COEFFICIENT OF DETERMINATION ........................................................................... 18
1.5 THE RANK CORRELATION COEFFICIENT (R) .......................................................... 20
1.6 TIED RANKINGS .............................................................................................................. 22
1.7 TIME SERIES ANALYSIS ................................................................................................ 24
CHAPTER TWO: SAMPLING THEORY .............................................................................. 30
2.1 SAMPLING: ....................................................................................................................... 31
2.2 TYPES OF SAMPLING ..................................................................................................... 31
2.3 MEAN AND STANDARD DEVIATION IN SIMPLE SAMPLING OF ATTRIBUTES 32
2.4 LARGE SAMPLES: TESTING THE SIGNIFICANCE FOR A SINGLE
PROPORTION ......................................................................................................................... 32
CHAPTER THREE: TEST OF HYPOTHESIS...................................................................... 35
3.1 INTRODUCTION:- ............................................................................................................ 36
3.2 TRADITIONAL METHOD ............................................................................................... 37
3.3 NULL AND ALTERNATIVE HYPOTHESIS .................................................................. 37
3.4 SIMPLE AND COMPOSITE HYPOTHESIS .................................................................... 37
3.5 TEST – STATISTIC ........................................................................................................... 38
3.6 ACCEPTANCE AND REJECTION REGIONS ................................................................ 38
3.7 TYPE I AND TYPE II ERRORS ...................................................................................... 38
4
