Producing models using probability theory and simulation

By Godfried Lawson

Textbook: “the Basic Practice of Statistics”

Second Edition with CD-ROM

Author: David S. Moore, Purdue University

Supplements for Students: Study Guide. Minitab Manual. Excel Manual. SPSS Manual.

SAS Manual. Telecourse Study Guide. TI-83 Graphing Calculator Manual.

Other Materials used:

Textbook: Elementary Statistics

A Step by Step Approach

Second edition

Author: Allan G. Bluman

Internet Resources: www.bbn.org/us.ap_statistics_outline_folder/course_outline.html

www.maths.uq.au/~gks/class/aa0.html

**CHAPTER FOUR:**

__Day 1__

**Section
4.1 Randomness:**

Parameter

Statistic

Population mean, sampling mean The population average ( mu ), the average
of the observations in the

sample ( x-bar )

Randomness and probability

Sampling variability. Different sample mean may produce different
mean value

Independent trials

Activity: Toss of a coin

Homework: Page 218-214 Ex 4.1-4.13

__Day 2__

Random numbers

Generating random integers on the TI-83. **
click here for the
activity folder**

Quiz #1 will cover section 4.1

Homework: Page 218-214 Ex 4.14-4.25
__Day 3__

**Section 4.2
Probability Models**

A probability model for a random phenomenon consists of sample S and a
assignment of

probabilities P.

Sample space: The sample space S of a random phenomenon is the set of all
possible outcomes.

Event

Probability model

Probability rule: addition rule for disjoint event ( mutually exclusive
)

Homework: page 221-231 Ex. 4.14-4.25
__Day 4__

Probabilities in a finite sample space.

Assign a probability to each individual outcome. These probabilities must
be numbers

between 0 and 1 and must have sum 1. the probability of any event is the
sum of the

probabilities of the outcomes making up the event.

Intervals of outcomes: p ( 0.3 < x < 0.5 ) ...

Properties of the normal distribution: The normal distribution is
a continuous , symmetric,

bell-shaped distribution of a variable.

1. Bell-shaped curve

2. The mean , median, mode are equal

3. The distribution curve is unimodal

4. The curve is symmetrical about the mean

5. The curve is continuous.

6. The curve never touch the x-axis

7. The total area under the normal distribution curve is equal to
1

8. The area under the normal curve that lies within one standard
deviation of the mean is

approximately 0.68; within two standard deviations , about 0.95 and within
three standard deviations,

about 0.997

Using tables of the normal distribution.

Draw the picture, shade the area decided, look up the z value in the table
to get the area.

Homework: page 232-236 Ex. 4.26-4.37
__Day 4__

Random variables: Random variable is a variable whose value is a numerical
outcome of a

random phenomenon.

Probability distribution: Probability distribution of a random variable
X tells us what values X can take and how

to assign probabilities to those values.

__Day 5__

Mid-chapter test review

Homework: Study guide worksheet.
__Day 6__

Mid-chapter test

__Day 7__

**Section 4.3 Sampling Distributions**

Statistical estimation and the law of large numbers

Draw observations at random from any population with finite mean: As the
number of observations drawn

increases, the mean of the observed values gets closer and
closer to the mean of the population.

Simulation of sample distributions: A method or procedure for exploring
and understanding the behavior of

complex processes by doing repeated experiments that resemble the actual
situation.

Simulation of probability distributions

Construction of sample distribution :TI-83 calculator activity: In this
activity, the learner will explore

sampling distribution through simulations of rolling dice. **Click
here for the activity folder**

__Day 8__

Mean and standard deviation of a sample mean

Unbiased estimator: Because the mean of the sample is equal to the mean
of the population

Homework: page 248-250 Ex. 4.38- 4.42

Central Limit Theorem.

Sampling distribution of a sample mean

Population N( mu, sigma),... sample N(mu, sigma/square root of n)

Homework: page 221-231 Ex. 4.43-4.55

** Day 9 **
Chapter Review Page 253

__Day 10__**
Chapter test**

__Why I used additional textbook__

I used the textbook :Elementary Statistics as additional material for
this project because the book presents a clear understanding of the multiplication
rules and makes shows the difference between the permutation and the combination.

The book also shows how the tree diagram is a devise used to list all
possibilities of a sequence of events in a systematic way. It is also used
to assign probabilities to each branch and with the multiplication rule,
find the probability of each branch.

__The positive aspect of the instructional unit__

This group project has helped me in many ways:

* I made an extra effort to read materials we did not learn
in the classroom..

* I designed my own lesson plan which includes the lecture, the
activities to reinforce the theory learned, the assessment

materials to check the level of mastery and I even
use other material which I found very useful to promote a quick

understanding of the topic.

* Over all this project has forced me to recall in a very short
period of time the topics I learned in my statistics class. Also I

feel more confident to teach this course.