Download effective fall 2001 - Tidewater Community College

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EFFECTIVE FALL 2009
DIVISION OF NATURAL SCIENCES AND MATHEMATICS
TIDEWATER COMMUNITY COLLEGE
VIRGINIA BEACH CAMPUS
COURSE PLAN
Course Number and Title
MATH 240 – Statistics
Lecture Hours
Lab Hours
3
0
Credit Hours
Submitted by:John Gallo, David Gray, Christy Hewett
Date 5/14/09
Richard Pugsley, Mario Scribner, Judy Williams
Approved by:
Copies:
_____________________________
Program Coordinator(s)
Date __________
_____________________________
Division Chairman
Date __________
Provost
Dean
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I. Course Description:
This course is designed to develop in the student, through the
study of the basic principles of probability and descriptive and
inferential statistics, an awareness and appreciation of the role
of statistics in the student=s daily life, to develop a
foundation for advanced study, and to develop the ability to
apply statistics in the student=s area of specialization.
II. Prerequisites:
MTH 158 or the equivalent of College Algebra
III. Introduction:
This course is designed to provide students with a basic
understanding of probability and statistics.
IV. Instructional Materials:
Textbook: Introductory Statistics, by Prem S. Mann; 2009;
ISBN 9780470545867; Wiley Custom Publishing.
Students must have the access code for WileyPLUS. The unique
passcode for each student is found at the front of new textbooks.
If a student registers online at
www.wileyplus.com/college/wileyplus he may purchase access and
find the whole text in electronic format.
MINITAB Statistical Software Release 15: available at no cost in
the Math Lab for all students; students may rent the software for
the semester through the Minitab web site
http://www.minitab.com/education/semesterrental/default.aspx
Handout on the uniform probability distribution (Chapter 6) is
attached at the end of this course plan
Scientific Calculator and/or programmable graphing calculator
with Mean and Standard Deviation function keys. Students
completing the prerequisite course should have such a calculator.
Anyone needing to purchase a calculator is encouraged to look at
the TI 30IIs
Supplementary Materials: Videotape series Against All Odds:
Inside Statistics available in the library or online at
http://www.learner.org/resources/series65.html
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V.
Course Objectives:
The student must master the following concepts:
A. Introduction (Ch 1 and Appendix A)
1.1 What is statistics?
1.2 Types of statistics
1.3 Population versus sample
1.4 Basic terms
1.5 Types of variables
1.6 Cross-section versus Time-series data
1.7 Sources of data
A.1 Sources of data
A.2 Sampling techniques
A.3 Designed experiment versus Observational study
1.8 Summation notation
B. Organizing and Graphing Data (Ch 2)
2.1 Raw data
2.2 Organizing and Graphing Qualitative Data
2.3 Organizing and Graphing Quantitative Data
2.4 Shapes of Histograms
2.5 Cumulative Frequency Distributions
2.6 Stem-and-leaf Plots
2.7 Dotplots
C. Numerical Descriptive Measures (Ch 3)
3.1 Measures of Central Tendency for Ungrouped Data
3.2 Measures of Dispersion for Ungrouped Data
A.3.1(Find mean and standard deviation with calculator in
statistical mode instead of emphasizing the
“shortcut formula”. Use the defining formula
initially for understanding of standard deviation as
“average difference of each x from the mean.”)
3.3 Mean, Variance, and Standard Deviation for Grouped Data
3.4 Measures of Position
3.5 Box-and-whisker Plot
D. Probability (Ch 4 and section 5.5)
4.1 Experiment, Outcomes, and Sample Spaces
4.2 Calculating Probability
4.3 Counting Rule
5.5 Factorials, Combinations, and Permutations
4.4 Marginal and Conditional Probabilities
4.5 Mutually Exclusive Events
4.6 Independent versus Dependent Events
4.7 Complementary Events
4.8 Intersection of Events and the Multiplication Rule
4.9 Union of Events and the Addition Rule
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E. Discrete Random Variables and Their Probability
Distributions (Ch 5)
5.1 Random Variables
5.2 Probability Distributions of a Discrete Random Variable
5.3 Mean of a Discrete Random Variable
5.4 Standard Deviation of a Discrete Random Variable
5.6 The Binomial Probability Distribution
(Show the connection to the binomial theorem studied in
Math 158)
5.7 The Hypergeometric Distribution *
5.8 The Poisson Distribution *
* sections taught primarily as contrast to binomial model
F. Continuous Random Variables and the Normal Distribution
Ch 6)
6.1 Continuous Probability Distribution
The Uniform Distribution
(Handout on the Uniform Distribution is located at the
end of this syllabus)
6.2 The Normal Distribution
6.3 The Standard Normal Distribution
6.4 Standardizing a Normal Distribution
6.5 Applications of the Normal Distribution
6.6 Determining the z and x Values for Known Area
6.7 The Normal Approximation to the Binomial Distribution
(as preparation for distribution of sample proportions)
G. Sampling Distributions (Ch 7)
7.1 Population and Sampling Distributions
7.2 Sampling and Nonsampling Errors
7.3 Mean and Standard Deviation of x-bar
7.4 Shape of the Sampling Distribution of x-bar
7.5 Applications of the Sampling Distribution of x-bar
7.6 Population and Sample Proportions
7.7 Mean, Standard Deviation, and Shape of the Sampling
Distribution of p-hat
H. Estimation of the Mean and Proportion (Ch 8)
8.1 Estimation: An Introduction
8.2 Point and Interval Estimates
8.3 Estimation of a Population Mean: σ known
8.4 Estimation of a Population Mean: σ unknown
8.5 Estimation of a Population Proportion: Large Samples
I. Hypothesis Tests About the Mean and Proportion (Ch 9)
8.1 Hypothesis Tests: An Introduction
8.2 Hypothesis Tests About µ: σ known
8.3 Hypothesis Tests About µ: σ not known
8.4 Hypothesis Tests About Proportion: large samples
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J. Correlation and Regression (Ch 13)
(Students should be able to create and interpret the
computer output rather than complete all the computations by
hand. If computation of the line and correlation coefficient
are taught, they should be done with a calculator capable of
finding the Σx and Σx2)
13.1 Simple Linear Regression Model
13.2 Simple Linear Regression Analysis
13.6 Linear Correlation
VII. Suggested Weekly Outline For Fall and Spring Semester:
Week 1: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8
Week 2: A.1, A.2, A.3, 2.1, 2.2, 2.3
Week 3: 2.4, 2.5, 2.6, 2.7, 3.1, 3.2,
Week 4: 3.3, 3.4, 3.5, 3.6 Test 1 (Chapters 1-3)
Week 5: 4.1, 4.2 4.3, 5.5, 4.4
Week 6: 4.5, 4.6, 4.7, 4.8, 4.9
Week 7: 5.1, 5.2, 5.3, 5.4
Week 8: 5.6, 5.7 or 5.8 Test 2 (Chapters 4-5)
Week 9: Uniform Distribution, 6.1, 6.2, 6.3
Week 10: 6.4, 6.5, 6.6, 6.7, 7.1, 7.2
Week 11: 7.3, 7.4, 7.5, 7.6, 7.7, 7.8 Test 3 (Chapters 6-7)
Week 12: 8.1, 8.2, 8.3
Week 13: 8.4, 9.1, 9.2
Week 14: 9.3, 9.4, 13.1
Week 15: 13.2, 13.6 Test 4 (Chapters 8-9)
Final Exam – as scheduled
VIII.
Suggested
Week 1:
Week 2:
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9:
Week 10:
Weekly Outline For Summer Semester:
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, A.1, A.2, A.3
2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 3.1, 3.2, 3.3
3.4, 3.5, 3.6, 4.1, 4.2, 4.3, 5.5 Test 1 (Chapters 1-3)
4.4, 4.5, 4.6, 4.7, 4.8, 4.9
5.1, 5.2, 5.3, 5.4, 5.6, 5.7 or 5.8 Test 2 (Chptrs 4-5)
Uniform Distribution, 6.1, 6.2, 6.3
6.4, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8
8.1, 8.2, 8.3, 8.4 Test 3 (Chapters 6-7)
9.1, 9.2, 9.3, 9.4 Test 4 (Chapters 8-9)
13.1, 13.2, 13.6 Final Exam
NOTE: Online students will follow the same schedule, but the four
tests will be replaced by proctored midterm and final exams as
well as online quizzes for each chapter.
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The Uniform Probability Distribution
Supplement to Chapter 6 (Revised May 2009)
The uniform probability distribution provides a model for continuous random variables that are
evenly distributed over a certain interval. There is no clustering of values around any one value;
instead, there is an even spread over the entire region of possible values.
Also see http://sofia.fhda.edu/gallery/statistics/lessons/lesson05-2.html
Properties of the uniform distribution:
1. The uniform probability density function is given by
1
f ( x)
, for c x d ,
d c
f ( x) 0, for all other values of x.
2. The graph of f(x) is given by
f(x)
1
d c
x
c
d
The distribution is a rectangular (uniform) shape with total area, A, of one
square unit. This requires that the width (vertical height) of the rectangle be
1
d c
Then the length of the rectangle (horizontal dimension) is d – c so that
1
A LW
d c
1.
d c
3. To find the probability that x lies between two given values, a and b, find the area of the
shaded rectangle.
f(x)
1
d c
c a
x
b d
b a
d c
d c
The probability can always be shown as a shaded portion of the uniform distribution
rectangle.
P(a
x b)
b a
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Properties of the uniform distribution (continued):
4. P( x a) 0
This is true for any continuous random variable, unlike the discrete random variables we
have already studied.
5. P(a x b) P(a x b) P(a x b) P(a x b)
Look at the area for each of the rectangles. Including or excluding the vertical line
segments does not change the area in the rectangle. (This is true for any continuous
random variable.)
c d
d c
and
. Note that we do
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not need this information in order to compute probabilities, but every distribution has a
mean and standard deviation.
6. The mean and standard deviation of f(x) are
Example of the Uniform Probability Distribution:
An unprincipled used car dealer sells a car to an unsuspecting buyer, even though the dealer
knows that the car will have a major breakdown within the next 6 months. The dealer provides a
warranty of 45 days on all cars sold. Let x represent the length of time until the breakdown
occurs. Assume that x is a uniform random variable with
values between 0 and 6 months.
a) Calculate the mean and standard deviation of x.
b) Calculate the probability that the breakdown occurs while the car is still under warranty.
Solution:
a) The parameters of x are c = 0 and d = 6 which allows us to create the picture of the
distribution, a rectangle above the interval [0, 6] with height y = f(x) = 1/(6-0) = 1/6
b)
Note that b is given as 45 days. The other times are given in
months. Thus 45days/30days is 1.5 months.
0 1.5
P(0
x 1.5)
1.5 0
6
1
6 0
0.25
Every continuous probability calculation should be accompanied by a picture of the area which
represents the probability.
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Uniform Probability Distribution Exercises:
1. A traffic engineer analyzes a model in which vehicle speeds are uniformly distributed between
a low of 30 mph and a high of 40 mph. Find the probability that the speed of a randomly selected
vehicle is
a. less than 35 mph;
b. greater than 32 mph;
c. between 33 mph and 39 mph.
2. The heights of pine seedlings grown by the State of Virginia have a uniform
distribution between a low of 23.5 inches and a high of 26.5 inches. What is the probability that a
seedling selected at random is greater than 24 inches?
3. WeFlyU Airlines quotes a one hour 52 minute flight time for its flights from
Cincinnati to Tampa. Suppose the actual flight times are uniformly distributed between the
quoted time and two hours and 10 minutes. What is the probability that a flight will be more than
10 minutes late?
4. The Home Sugar Company packages its product in bags labeled 5 pounds. The
packing machine actually follows a uniform distribution with weights varying
from a low of 4.98 pounds to a high of 5.14 pounds. Find the probability
that a randomly selected bag weighs
a. more than 5 pounds;
b. less than 4 pounds 12 ounces;
c. between 5 pounds and 5.1 pounds.
5. The time that patients must wait to see Dr. Derrick is uniformly distributed between 15 and 50
minutes.
a. Find the probability that a patient will have to wait at least a half hour to see the doctor.
b. What percentage of patients have to wait less than 20 minutes?
c. Find the probability that a patient will wait exactly 20 minutes.
d. What is the probability that a patient will wait more than an hour?
* e. What is the 90th percentile for the waiting time? In other word, 90% of the patients spend no
more than this amount of time in the waiting room?
* f. Given that a patient has already waited 30 minutes, what is the probability that he will have
to wait more than 40 minutes?
Answers to Exercises
1a. 0.500
2. 0.833
3. 0.444
b. 0.800
c. 0.600
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4a. 0.875
b. 0
c. 0.625
5a. 0.571
b. 14.3%
c. 0
d. 0
e. 46.5 minutes
f. 0.500