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Math 301
Introduction to Probability and Statistics
Spring 2009
Section 001 3:00 to 4:30, M W
Instructor: Dr. Chris Edwards
Classroom: Swart 127
Phone: 424-1358 or 948-3969
Office: Swart 123
Text: Probability and Statistics, 7th edition, by Devore.
Required Calculator: TI-83, TI-83 Plus, or TI-84 Plus, by Texas Instruments. Other TI
graphics calculators (like the TI-86) do not have the same statistics routines we will be using and
may cause you troubles.
Catalog Description: Elementary probability models, discrete and continuous random
variables, sampling and sampling distributions, estimation, and hypothesis testing. Prerequisite:
Mathematics 172 with a grade of C or better.
Course Objectives: The goal of statistics is to gain understanding from data. This course
focuses on critical thinking and active learning. Students will be engaged in statistical problem
solving and will develop intuition concerning data analysis, including the use of appropriate
technology. Specifically students will develop
•
an awareness of the nature and value of statistics
•
a sound, critical approach to interpreting statistics, including possible misuses
•
facility with statistical calculations and evaluations, using appropriate technology
•
effective written and oral communication skills
Grading: Final grades are based on these 300 points:
Exam 1
Topic
Summaries, Probability
Points
50 pts.
Tentative Date
March 9
Exam 2
Exam 3
Group Presentations
Homework
Distributions
Inference
15 Points Each
10 Points Each
50 pts.
50 pts.
60 pts.
90 pts.
April 15
May 13
Various
Mostly Weekly
Chapters
1, 2, 3.1 to 3.3,
4.1 to 4.2
3, 4, 5
7, 8
Final grades are assigned as follows:
270 pts. or more
255 pts. or more
240 pts. or more
225 pts. or more
210 pts. or more
180 pts. or more
179 pts. or less
A (90 %)
AB (85 %)
B (80 %)
BC (75 %)
C (70 %)
D (60 %)
F
Homework: I will collect three homework problems approximately once a week. The due dates
are listed on the course outline below. While I will only be grading three problems, I presume
that you will be working on many more than just the three I assign. I suggest that you work
together in small groups on the homework for this class. What I expect is a well thought-out,
complete discussion of the problem. Please don't just put down a numerical answer; I want to
see how you did the problem. (You won't get full credit for just numerical answers.) The
method you use is much more important to me than the final answer.
Presentations: There will be four presentations, each worth 15 points. The descriptions of the
presentations are in the Day By Day Notes. I will assign you to your groups for these
presentations randomly, because I want to avoid you having the same members each time. I
expect each person in a group to contribute to the work; however, you can allocate the work in
any way you like. If a group member is not contributing, see me as soon as possible so I can
make a decision about what to do. The topics are: 1 - Displays (February 18). 2 - Probability
(March 4). 3 - Central Limit Theorem (April 21). 4 - Statistical Hypothesis Testing (May 11).
Office Hours: Office hours are times when I will be in my office to help you. There are many
other times when I am in my office. If I am in and not busy, I will be happy to help. My office
hours for Spring 2009 semester are 10:20 to 11:00, Monday, Tuesday, Wednesday, and Friday,
and 3:00 to 4:00 Tuesday, or by appointment.
Philosophy: I strongly believe that you, the student, are the only person who can make yourself
learn. Therefore, whenever it is appropriate, I expect you to discover the mathematics we will be
exploring. I do not feel that lecturing to you will teach you how to do mathematics. I hope to be
your guide while we learn some mathematics, but you will need to do the learning. I expect each
of you to come to class prepared to digest the day’s material. That means you will benefit most
by having read each section of the text and the Day By Day notes before class.
My idea of education is that one learns by doing. I believe that you must be engaged in the
learning process to learn well. Therefore, I view my job as a teacher as not telling you the
answers to the problems we will encounter, but rather pointing you in a direction that will allow
you to see the solutions yourselves. To accomplish that goal, I will work to find different
interactive activities for us to work on. Your job is to use me, your text, your friends, and any
other resources to become adept at the material. Remember, the goal is to learn mathematics, not
to pass the exams. (Incidentally, if you have truly learned the material, the test results will take
care of themselves.)
Monday
Wednesday
February 2 Day 1
Introduction, Random Sampling
Section 1.1
February 4 Day 2
Graphical Summaries
Section 1.2
February 9 Day 3
Numerical Summaries
Sections 1.3 to 1.4
February 11 Day 4
Homework 1 Due
Intro to Probability
Sections 2.1 to 2.2
February 16 Day 5
Permutations, Combinations
Section 2.3
February 18 Day 6
Presentation 1
Trees
Section 2.4
February 23 Day 7
Homework 2 Due
Bayes', Independence
Section 2.5
February 25 Day 8
Coins, Dice, RV's
Sections 3.1 to 3.3
March 2 Day 9
Homework 3 Due
Continuous Distributions
Sections 4.1 to 4.2
March 4 Day 10
Presentation 2
Normal
Section 4.3
March 9 Day 11
March 11 Day 12
Normal Problems
Section 4.3
Exam 1
March 16 Day 13
Gamma
Section 4.4
March 18 Day 14
Homework 4 Due
Probability Plots, Binomial
Sections 4.6, 3.4
March 30 Day 15
Binomial
Section 3.4
April 1 Day 16
Homework 5 Due
Hypergeometric, Negative Binomial
Section 3.5
April 6 Day 17
Normal Approx to Binomial
Section 4.3
April 8 Day 18
Homework 6 Due
Central Limit Theorem
Sections 5.3 to 5.4
April 13 Day 19
More CLT, Linear Combinations
Sections 5.4 to 5.5
April 15 Day 20
Exam 2
April 20 Day 21
m&m’s
Sections 7.1 and 7.2
April 21 Day 22
Presentation 3
Intro to Hypothesis Testing
Section 8.1
April 27 Day 23
Homework 7 due
Z-Procedures
Sections 7.3 and 8.2
April 29 Day 24
Testing Simulations
Section 8.4
May 4 Day 25
Homework 8 Due
t-procedures
May 6 Day 26
Proportions
Sections 7.2 and 8.3
Section 8.2
May 11 Day 27
Homework 9 Due
Presentation 4
Review
May 13 Day 28
Exam 3
Homework Assignments: (subject to change if we discover difficulties as we go)
Homework 1, due February 13
1)
Exercise 72 Page 43
2)
Consider a sample x1, x 2 ,..., x n and suppose that the values of x and s have been
calculated. Let y i = x i − x and zi = y i /s for all i's. Find the means and standard
deviations for the y i ' s and the zi ' s .
3)
Specimens of three different types of rope wire were selected, and the fatigue limit was
determined for each specimen. Construct a comparative box plot and a plot with all three
quantile plots superimposed. Comment on the information each display contains. Also
explain which graphical display you prefer for comparing these data sets.
Type 1 350
384
350
391
350
391
358
392
370
370
370
371
371
372
372
Type 2 350
380
354
383
359
388
363
392
365
368
369
371
373
374
376
Type 3 350
379
361
380
362
380
364
392
364
365
366
371
377
377
377
Homework 2, due February 23
1)
Exercise 14 Pages 57-58
2)
Exercise 40 Page 66
3)
Exercise 42 Page 67
Homework 3, due March 2
1)
In a Little League baseball game, suppose the pitcher has a 50 % chance of throwing a
strike and a 50 % chance of throwing a ball, and that successive pitches are independent
of one another. Knowing this, the opposing team manager has instructed his hitters to not
swing at anything. What is the chance that the batter walks on four pitches? What is the
chance that the batter walks on the sixth pitch? What is the chance that the batter walks
(not necessarily on four pitches)? Note: in baseball, if a batter gets three strikes he is out,
and if he gets 4 balls he walks.
2)
A car insurance company classifies each driver as good risk, medium risk, or poor risk.
Of their current customers, 30 % are good risks, 50 % are medium risks, and 20 % are
poor risks. In any given year, the chance that a driver will have at least one citation is 10
% for good risk drivers, 30 % for medium risk drivers, and 50 % for poor risk drivers. If
a randomly selected driver insured by this company has at least one citation during the
next year, what is the chance that the driver was a good risk? A medium risk?
3)
Exercise 24 Pages 99-100
Homework 4, due March 20
1)
Use the following pdf and find a) the cdf b) the mean and c) the median of the
distribution.
 1 (4 − x 2 ) −1 ≤ x ≤ 2
f (x) =  9
0
otherwise

2)
Exercise 38 Page 155
3)
Suppose the time it takes for Jed to mow his lawn can be modeled with a gamma
distribution using α = 2 and β = 0.5. What is the chance that it takes at most 1 hour for
Jed to mow his lawn? At least 2 hours? Between 0.5 and 1.5 hours?
Homework 5, due April 1
1)
Exercise 94 Page 179
2)
Exercise 54 Page 114
3)
Exercise 62 Page 115
Homework 6, due April 10
1)
A second stage smog alert has been called in a certain area of Los Angeles county in
which there are 50 industrial firms. An inspector will visit 10 randomly selected firms to
check for violations of regulations. If 15 of the firms are actually violating at least one
regulation, what is the pmf of the number of firms visited by the inspector that are in
violation of at least one regulation? Find the Expected Value and Variance for your pmf.
2)
A couple wants to have exactly two girls and they will have children until they have two
girls. What is the chance that they have x boys? What is the chance they have 4 children
altogether? How many children would you expect this couple to have?
3)
Let X have a binomial distribution with n = 25. For p = .5, .6, and .9, calculate the
following probabilities both exactly and with the normal approximation to the binomial.
a) P(15 ≤ X ≤ 20) b) P(X ≤ 15) c) P(20 ≤ X) Comment on the accuracy of the normal
approximation for these choices of the parameters.
Homework 7, due April 27
1)
There are 40 students in a statistics class, and from past experience, the instructor knows
that grading exams will take an average of 6 minutes, with a standard deviation of 6
minutes. If grading times are independent of one another, and the instructor begins
grading at 5:50 p.m., what is the chance that grading will be done before the 10 p.m.
news begins?
2)
A student has a class that is supposed to end at 9:00 a.m. and another that is supposed to
begin at 9:10 a.m. Suppose the actual ending time of the first class is normally
distributed with mean 9:02 and standard deviation 1.5 minutes. Suppose the starting time
of the second class is also normally distributed, with mean 9:10 and standard deviation 1
minute. Suppose also that the time it takes to walk between the classes is a normally
distributed random variable with mean 6 minutes and standard deviation 1 minute. If we
assume independence between all three variables, what is the chance the student makes it
to the second class before the lecture begins?
3)
A 90 % confidence interval for the true average IQ of a group of people is (114.4, 115.6).
Deduce the sample mean and population standard deviation used to calculate this
interval, and then produce a 99 % interval from the same data.
Homework 8, due May 4
1)
A hot tub manufacturer advertises that with its heating equipment, a temperature of
100°F can be achieved in at most 15 minutes. A random sample of 32 tubs is selected,
and the time necessary to achieve 100°F is determined for each tub. The sample average
time and sample standard deviation are 17.5 minutes and 2.2 minutes, respectively. Does
this data cast doubt on the company's claim? Calculate a P-value, and comment on any
assumptions you had to make.
2)
A sample of 50 lenses used in eyeglasses yields a sample mean thickness of 3.05 mm and
a population standard deviation of .30 mm. The desired true average thickness of such
lenses is 3.20 mm. Does the data strongly suggest that the true average thickness of such
lenses is undesirable? Use α = .05. Now suppose the experimenter wished the
probability of a Type II error to be .05 when µ = 3.00. Was a sample of size 50
unnecessarily large?
3)
Exercise 24 Page 305
Homework 9, due May 11
1)
Fifteen samples of soil were tested for the presence of a compound, yielding these data
values: 26.7, 25.8, 24.0, 24.9, 26.4, 25.9, 24.4, 21.7, 24.1, 25.9, 27.3, 26.9, 27.3, 24.8,
23.6. Is it plausible that these data came from a normal curve? Support your answer.
Now calculate a 95% confidence interval for the true average amount of compound
present. Comment on any assumptions you had to make.
2)
Exercise 20 Page 269
3)
Exercise 38 Page 310
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Last updated January 11, 2009