Producing models using probability theory and simulation
By Godfried Lawson

Material:
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,
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

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.

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