Math 301
Introduction to Probability and Statistics
Spring 2009
Section 001 3:00 to 4:30, M W
Instructor: Dr. Chris Edwards Phone: 424-1358 or 948-3969 Office: Swart 123
Classroom: Swart 127 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:
|
|
Topic |
Points |
Tentative Date |
Chapters |
|
Exam 1 |
Summaries, Probability |
50 pts. |
March 9 |
1, 2, 3.1 to 3.3, 4.1 to 4.2 |
|
Exam 2 |
Distributions |
50 pts. |
April 15 |
3, 4, 5 |
|
Exam 3 |
Inference |
50 pts. |
May 13 |
7, 8 |
|
Group Presentations |
15 Points Each |
60 pts. |
Various |
|
|
Homework |
10 Points Each |
90 pts. |
Mostly Weekly |
|
Final grades are
assigned as follows:
270 pts. or more A
(90 %)
255 pts. or more AB
(85 %)
240 pts. or more B
(80 %)
225 pts. or more BC
(75 %)
210 pts. or more C
(70 %)
180 pts. or more D
(60 %)
179 pts. or less 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 |
February 4 Day
2 |
|
February 9 Day 3 |
February 11 Day 4 |
|
February 16 Day 5 |
February 18 Day 6 |
|
February 23 Day 7 |
February 25 Day 8 |
|
March 2 Day 9 |
March 4 Day
10 |
|
March 9 Day 11 |
March 11 Day
12 |
|
March 16 Day 13 |
March 18 Day
14 |
|
March 30 Day 15 |
April 1 Day
16 |
|
April 6 Day 17 |
April 8 Day
18 |
|
April 13 Day 19 |
April 15 Day
20 |
|
April
20 Day 21 |
April 21 Day 22 |
|
April 27 Day 23 |
April 29 Day
24 |
|
May 4 Day 25 Section 8.2 |
May 6 Day
26 |
|
May 11 Day 27 |
May 13 Day
28 |
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 
and suppose that the values of 
and s have been calculated. Let 
and 
for all i's. Find
the means and standard deviations for the 
and the 
.
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
1 350 350 350 358 370 370 370 371 371 372 372 384 391 391 392
Type
2 350 354 359 363 365 368 369 371 373 374 376 380 383 388 392
Type
3 350 361 362 364 364 365 366 371 377 377 377 379 380 380 392
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.
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 a
= 2 and b = 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 a = .05. Now suppose the experimenter wished the
probability of a Type II error to be .05 when m =
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