US ID:9015

LEARNER WORKBOOK
APPLY KNOWLEDGE OF STATISTICS AND
PROBABILITY TO CRITICALLY
INTERROGATE AND EFFECTIVELY
COMMUNICATE FINDINGS ON LIFE
RELATED PROBLEMS

1|Page
Learner Information:
Details Please Complete this Section
Name & Surname:
Organisation:
Unit/Dept:
Facilitator Name:
Date Started:
Date of Completion:

Copyright
All rights reserved. The copyright of this document, its previous editions and
any annexures thereto, is protected and expressly reserved. No part of this
document may be reproduced, stored in a retrievable system, or
transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording or otherwise without the prior permission.

2|Page
 OVERVIEW

About the This Learner Exercise Workbook has been designed and
Learner developed to evaluate learners’ level of understanding of
Workbook the APPLY KNOWLEDGE OF STATISTICS AND
PROBABILITY TO CRITICALLY INTERROGATE AND
EFFECTIVELY COMMUNICATE FINDINGS ON LIFE
RELATED PROBLEMS.
It forms part of a series of Learner Workbooks that have
been developed for

Purpose The purpose of this Learner Exercise Workbook is to

evaluate learners understanding on the specific outcomes
and/or assessment criteria of the following SAQA Registered
Unit Standards:

US No US Title Leve Credi

l ts

9015 Apply knowledge of statistics and 4 6

probability to critically interrogate and
effectively communicate findings on life
related problems
Context This assessment represents the Formative Assessment
component of the Apply knowledge of statistics and
probability to critically interrogate and effectively
communicate findings on life related problems for the
FURTHER

and should be completed in the classroom/training room.

Resources The following are resources needed for this assessment:

1. Learner Guide; and
2. Assessment Preparation.

3|Page
Instructions Facilitators will be required to:
to  Explain the completion of the workbook to each
Facilitators learner; and
 Interview the learner on similar questions, should
he/she not be able to write.
Instructions Learners will be required to:
to Learners  Complete the workbook as per the instructions;
 Ensure that all questions are completed;
 Ensure that the completion of the workbook is their
own work;
 Ensure that all annexure are attached to the
workbook and clearly referred to;

Assessment Learners are required to complete this assessment within

Time the allocated time frame of.... hours.
Total Mark This formative assessment carries a total mark of _ points.
In order to meet the pass mark, learners are required to
achieve a minimum of 80% of the total marks.
Equipment Learners are required to have the following equipment in
order to complete this workbook:
 Pen and Pencil;
 Ruler; and
 Exam Pad – for additional paper.

4|Page
 GENERAL INFORMATION

LEARNER DETAILS
Learner Full
Names
Learner ID No.:
Organisation:
Unit/Dept:
Contact Details: Telephone /Cell Email Address:
Numbers:

WORKSHOP DETAILS
Workshop
Venue:
Facilitator
Name:
Date Started:
Date Completed:

ASSESSMENT PREPARATION CHECKLIST

DESCRIPTION YE NO COMMENTS/
S CONTINGENCY
This assessment is a formative assessment and it is
based on the outlined unit standard/s for the Apply
knowledge of statistics and probability to
critically interrogate and effectively
communicate findings on life related problems
module.
Your assessment evidence for Apply knowledge of
statistics and probability to critically
interrogate and effectively communicate
findings on life related problems module needs

5|Page
to be submitted on....... (day) of...............
(month)...........(year) at the following
address/place...............................................................
.
You will be assessed based on the outlined Unit
Standards. The assessment activities are linked to
specific outcomes/assessment criteria of the outlined
Unit Standards.
To determine your competence level, the following
are the methods to be used for this assessment:
1. .....................................................
2. .....................................................
To be declared competent on Apply knowledge of
statistics and probability to critically
interrogate and effectively communicate
findings on life related problems module
(formative assessment), you should have obtained at
least 80% of the total mark of this assessment.
You will be provided with detailed feedback on your
performance of this assessment as follows:
1. Written Feedback
2. Verbal Feedback
Should you be declared “not yet competent” on this
assessment, you will be entitled for re-assessment
opportunity/ies.
You will be required to re-submit evidence (only for
areas) you were declared not yet competent. A date
for re-submission will be agreed with the assessor.
You will be entitled to lodge an appeal should you not
be satisfied with the assessment decision of your
assessment.
You will be required to provide the assessor feedback
on assessment procedure – this is to assist in
improving the assessment practices.
Your results of assessment and portfolio of evidence

6|Page
information will not be provided to any person
without your written consent.

7|Page
 Learner’s Declaration

I…………………………………………………………………………………………….herewith declare that I

am ready for the assessment, that we have reviewed the assessment preparation and plan, I
understand the assessment process and I am happy that the assessment will be conducted in
a fair manner.
Learner Signature: Date: Facilitator Date:
Signature:

8|Page
 Apply knowledge of statistics and

Learning Unit 1
probability to critically interrogate
and effectively communicate
findings on life related problems

UNIT STANDARD NUMBER : 9015

LEVEL ON THE NQF : 4
CREDITS : 6
FIELD : Physical, Mathematical, Computer and Life Sciences
SUB FIELD : Mathematical Sciences

This Unit Standard is designed to provide credits towards the

PURPOSE: mathematical literacy requirement of the NQF at Level 4. The essential
purposes of the mathematical literacy requirement are that, as the
learner progresses with confidence through the levels, the learner will
grow in:
 A confident, insightful use of mathematics in the management of the
needs of everyday living to become a self-managing person
 An understanding of mathematical applications that provides insight into
the learner`s present and future occupational experiences `and so
develop into a contributing worker
 The ability to voice a critical sensitivity to the role of mathematics in a
democraticthe
Complete society and so become
following a participating
questions citizen.
as per instructions
People credited with this unit standard are able to:
provided
 Critique and use techniques for collecting, organising and representing
data.
 Use theoretical and experimental probability to develop models, make
predictions and study problems.
 Critically interrogate and use probability and statistical models in
problem solving and decision making in real-world situations.

LEARNING ASSUMED TO BE IN PLACE:

The credit value is based on the assumption that people starting to learn towards this unit
standard al-e competent in Mathematical Literacy and Communications at NQF level 3.
Activities

1.1 Identify 3 situations or issues in your workplace that can be dealt

with through statistical methods and in each case say what type of routine
statistics you would gather:

9|Page
Situation/issue Type of Statistics

1.2 Explain how forecasting plays a role in your business unit and organisation:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2. Read the following article written by the statistician-general of SA,
and then answer the questions that follow:

Civil judgments for debt down 15.8% in first quarter

June 23, 2005
By PaliLehohla
Not all data released by Statistics SA make the headlines. However, some of the
less prominent statistical releases contain important insights, which shed light on
trends and developments in society as a whole and the economy in particular.

10 | P a g e
For example, each month Stats SA releases data on civil cases for debt. This
survey, which covers a sample of magistrates' offices, collects information
regarding civil cases recorded, civil summonses issued and civil judgments
recorded.
Its provides information on the extent of unpaid debt in South Africa, which is used
by the private and public sectors as an indicator of economic performance.
Each month the survey covers the number of civil cases recorded; the number of
civil summonses issued for debt; the number of civil judgments recorded for debt;
and the value of civil judgments recorded for debt.
The most recent data released in this series reports on three periods: the month of
March 2005; change over the period March 2004 to March 2005; and change
between the first quarter of 2004 compared with the first quarter of 2005.
In most areas monitored there was a decrease in the indicators of debt. The total
number of civil summonses issued for debt in the first quarter of 2005 decreased by
16.4 percent compared with the first quarter of 2004.
The big contributors to this decrease were summonses issued in respect of money
lent (down 6 percentage points), promissory notes (down 2.3 percentage points),
"other" services (down 2.3 percentage points), goods sold on open account (down
1.7 percentage points) "other" debts (down 1.7 percentage points) and rent (down
1.4 percentage points).
Following this pattern, the total number of civil judgments recorded for debt for the
first quarter of 2005 decreased by 15.8 percent compared with the first quarter of
2004.
The contributors to this decrease were civil judgments in respect of money lent
(down 5.1 percentage points), promissory notes (down 2.4 percentage points), rent
(down 2.2 percentage points), and "other" debts (down 1.8 percentage points).
The total value of civil judgments recorded for debt for the first quarter of 2005
decreased by 5.3 percent compared with the first quarter of 2004.
The major contributors to this decrease were civil judgments recorded in respect of
promissory notes (down 4.1 percentage points) and "other" debts (down 2
percentage points).
However, this decrease was slightly counteracted by an increase in civil judgments
recorded in respect of professional services (1 percentage point).
Turning to the month of March this year, 65 406 civil judgments for debt amounting

11 | P a g e
to R521 million were recorded.
The largest contributors to this amount were civil judgments relating to money lent
(R155.3 million, or 29.8 percent), "other" debts (R135 million, or 25.9 percent) and
promissory notes (R77.4 million, or 14.9 percent). During this month, 108 302 new
civil summonses for debt were issued.
Comparative data released as at March 2005 show a decline in the number of civil
summonses issued for debt between March 2001 and March 2005. Peaking in
December 2002 at over 159 000, the March 2005 figure has fallen to just over 108
000.
The number of civil judgments recorded for debt reached a high of approximately
105 000 in mid-2003, falling to approximately 65 400 in March 2005.
Today Stats SA releases the latest data on civil cases for debt, which will reflect
the position as at April 2005. Although a lesser-known indicator of trends in the
economy, this monthly release provides important insights into economic
performance.
PaliLehohla is the statistician-general and head of Statistics SA. For more
information on Stats SA and its outputs, including the latest statistics of civil cases
for debt, visit www.statssa.gov.za, or contact user services on (012) 310-8600

12 | P a g e
2.1 Explain what is meant by a “trend” (paragraph 1):
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

2.2 What “trend” has been identified by Stats SA according to this article?
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2.3 Explain what is meant by a “series” (paragraph 5). Refer specifically to the
series mentioned in the article:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2.4 List the indicators of debt mentioned in the article:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

13 | P a g e
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2.5 Explain the difference between a census and a sample:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2.6 You want to undertake a statistical study of absenteeism in your company.
Would you take a census or a sample? Give reasons for your answer.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2.7 In order to collect a representative sample from your team/ business unit,
how many members would you have to survey? Explain how you arrived at that
figure.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

14 | P a g e
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2.8 In order to collect a representative sample from your company, how many
employees would you have to survey? Explain how you arrived at that figure.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

15 | P a g e
3.1 Group work (30 minutes):
Choose a topic that relates to your class, e.g. you want to determine the number of
people who are in favour of abortion among the class members, or the number of
happily married learners, or the education level of the learners in the class, in fact,
any topic of your choice. Draw up a questionnaire using the dichotomous key
(about five sets of questions), do a quick survey and present your findings to the
class:

Topic:

Questionnaire:

Question Yes/no Go to/

completed
1.
A.

B.

2.
A.

B.

3.
A.

B.

4.
A.

B.

16 | P a g e
5.
A.

B.

3.2 Group work (20 minutes):

Draw up a 10-point checklist that will help you determine if a questionnaire meets
the criteria as set out in your Learner Guide:

17 | P a g e
3.3 Likert scale
A survey attempted to evaluate student interest about a range of classroom topics.
Students were asked to rank their interest in various potential topics according to
this scale:
10 if they felt a topic was very interesting
6 if they felt a topic was above average interest
4 if they felt a topic was below average interest
1 if they felt a topic was not worth studying in class

Please note that only four responses were permitted: 10, 6, 4, and 1. Is this an
acceptable survey design? Explain your answer:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
4. When interviewing your team for the purposes of a survey, do you think that
there could possibly be bias from either your side or their side? Discuss possible
reasons for the bias, based on the information in the Learner Guide. Add any other
causes of bias that you may be aware of.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

18 | P a g e
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

5.1 Here are the test scores of a class of learners:

100, 100, 99, 98, 92, 91, 91, 90, 88, 87, 87, 85, 85, 85, 80, 79, 76, 72, 67,
66, 45

a) What is the average score (mean) of the class for this test?
b) Is the sequence written in ascending or descending order?
c) Determine the median score
d) James obtained a mark of 90 and Petrus obtained a mark of 79 for the
test. How would you describe their results in relation to the mean?
e) In order to get a better idea of how a given data point relates to other
data, it is important to get an idea of how spread out the data are. One
way of doing this is by using the range. The range is the distance
between the highest and lowest data points in a set. What is the ‘range’ of
the scores for this test?
a)

b)

c)

d)

e)

19 | P a g e
5.2 Group work (15 minutes): Find out how old each learner in the class is

5.2.1 Planning phase:

 First decide on the quickest and most effective way to obtain the required
information
 How can you ensure that the information is accurate and representative?
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5.2.2 Obtain and sort data: Calculate the average age (mean) of the learners
in this class.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5.2.3 Calculate the median of the ages of all the learners. Show the sequence in
ascending order:
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

20 | P a g e
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5.2.4 Analyse data:What conclusions can you reach based on the data?
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
5.2.5 Reflect on the process you followed to obtain the information:
 Was it effective?
 Were respondents cooperative?
 What would you do differently next time?
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

21 | P a g e
6.1 Draw a reasonably accurate pie chartby hand based on the following data:
 Absenteeism due to transport problems 108º
 Absenteeism due to illness 162º
 Absenteeism due to training 45º
 Absenteeism due to family commitments 45º

Give your chart a title that accurately reflects the kind of data represented;

Title:
________________________________________________________________________________

Legend:____________________________________________________________________________
_
6.2 Give an example of the type of data in the workplace that you would
represent with a) a bar chart, b) a line chart and c) a scatter diagram:
a)

b)

c)

22 | P a g e
7. Read the following article written by the statistician-general of SA, paying
particular attention to his explanation of the limitations of statistical
information, and then answer the questions that follow:

New employment survey makes three improvements

By PaliLehohla
This article was originally published in the Business Report on 07 July 2005
Statistics SA continues to improve the quality of its statistics. The quarterly
employment statistics (QES) survey was published for the first time on June 28.
This survey replaces the quarterly survey of employment and earnings (SEE) which
in turn replaced the survey of total employment and earnings (STEE).

There are important differences between these surveys, all aimed at improving the
quality of the information. First, the STEE was drawn from the initial business
address register, which was not based on the comprehensive taxation database
that the current surveys are based on. It reported formal employment in the non-
agricultural sector of 4.7 million people.

Second, the recently introduced QES covers all employing enterprises in the formal
non-agricultural business sector registered for income tax, whereas the SEE was
restricted to enterprises registered for VAT, with an annual turnover of R300 000
or more.

The increase in the coverage of businesses in the QES results in extensive

coverage of the formal labour market, as most small businesses are now
included in the estimates as well.

For the quarter to December 2004, the SEE reported employment of 6.559
million people, compared with the estimate of 7.075 million in the QES.

Third, the definition of employees has been brought in line with International
Labour Organisation (ILO) definitions and concepts. Previously, the SEE included
working proprietors and own account workers in the estimates of employment, in
addition to the employees of an enterprise. This did not allow for the meaningful

23 | P a g e
calculation of estimates for average monthly earnings of employees.

However, the QES restricts the coverage to employing businesses only, therefore
excluding working proprietors in the estimates. It is therefore now possible to
provide estimates for employment and earnings as well, as the survey is in
accordance with ILO definitions and recommendations.

The SEE and the QES are not comparable because of these
improvements. The estimates for employment for the quarter to December,
published on June 28 in the QES, show a difference of about 500 000 employees.
This was largely due to the extended coverage of the QES survey, made possible
by improvements to the business frame that I reported on in earlier articles.

The drop in employment in the first quarter was largely caused by seasonal
factors, with many people being employed for the December period only. The
published results do not take this seasonality into account as it is not
possible to develop seasonally adjusted estimates for a series that has
only been published for two periods.

As the series progresses and more results become available, it will become
possible to get a clear insight into the labour market by using the QES survey
estimates.

Furthermore, the major contributors to differences in employment levels

between the QES for December and the SEE for December are the
financial intermediation, insurance, real estate and business services
industry, up about 40 percent; the construction industry, up about 30
percent; and the transport, communication and storage industry, up
about 50 percent. These increases are mainly due to the QES survey's
coverage of small businesses in these industries. The SEE did not cover
many of these small businesses.

Information regarding employers, employees and the self-employed can be

24 | P a g e
obtained from the six-monthly labour force survey, conducted among 30
000 households countrywide. The results of this survey should be read in
conjunction with those of the QES, as they all inform on the dynamics in the labour
market.
Over time, by using register-based frames, Stats SA has continued to provide a
more representative picture of the economic and the population dynamics of the
country.

The underlying purpose of statistics is to inform users and policy, and

statistics should not be misconstrued to suit specific situations. Extreme caution
should be exercised when commenting on a time series that has only two data
points and the differences between relevant series should be kept in mind at all
times.
PaliLehohla is the statistician-general and head of Statistics SA. For more
information on Stats SA and its outputs visit www.statssa.gov.za, or contact
user services on (012) 310-8600

7.1 Explain how the representative sample has grown from 4.7 million (STEE
findings) to 6.559 (SEE) to the current 7.075 million (QES findings):
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
7.2 What categories of workers have been excluded from QES and why?
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

25 | P a g e
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

7.3 Information regarding employers, employees and the self-employed is

obtained by conducting surveys:
a) What is the frequency of these surveys?
b) Why should they be conducted frequently?
c) What is the size of the sample?
d) Do you think that it is a representative sample? Give a reason for your
answer.
e) What are some of the problems regarding choosing a sample of this
nature?
a)

b)

c)

d)

e)

26 | P a g e
7.3 What are the limitations of a time series that has only two data points?
(par.14)?
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________

On a lighter note:
"If a statistician had her hair on fire and her feet in a block of ice, she would say
that 'on average' she felt good."

27 | P a g e
 SELF-ASSESSMENT

The learner must make use of the following self-evaluation checklist to rate himself
against the learning outcomes of this particular training module in establishing the
level of mastery of the information.
1. Not able to comply
2. Reasonable compliance (Not acceptable for final evaluation)
3. Able to comply fully

LEARNING OUTCOMES 1 2 3
1
2
3
4

____________________________________________
________________________________
Learner Signature Date

____________________________________________ ________________________________
Facilitators’ Signature Date

28 | P a g e
 ASSESSMENT FEEDBACK REPORT

FACILITATOR FEEDBACK & REMARKS

ASSESSMENT JUDGEMENT

Learner’s Total Mark: Requirements met

Requirements not met

Action/s required:

By when:

LEARNER FEEDBACK & COMMENTS

DECLARATION BY THE FACILITATOR

I ……………………………………………............. (Facilitator) hereby certify that I have

examined the learner workbook and I am satisfied with the evidence provided by
the learner.

29 | P a g e
 DECLARATION BY LEARNER

I, …………………………………………………………………….declare that I am satisfied

that the feedback given to me by the Facilitator was relevant, sufficient and done in
a constructive manner. I accept the assessment judgment and have no further
questions relating to this particular assessment event.

Learner Date Facilitator Date

DECLARATION BY THE ASSESSOR

I ……………………………………………............. (Assessor) hereby certify that I have

examined the learner workbook and I am satisfied with the Facilitator Judgment of
this assessment.

Assessor Date Moderator Date

30 | P a g e ALL COPYRIGHT RESERVED