Math 301
Introduction to Probability and Statistics
Fall 2007
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: Engineering Statistics, 4th
edition, by Montgomery,
Runger, and Hubele.
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. |
October 10 |
1-3.4, 3.7 |
|
Exam 2 |
Distributions |
50 pts. |
November 12 |
3 |
|
Exam 3 |
Inference |
50 pts. |
December 12 |
4 |
|
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 3 homework problems approximately once a
week. The due dates are listed on
the course outline below. While I
will only be grading 3 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. To aid in your study
groups, I will be distributing a class roll.
Presentations: There
will be four presentations, each worth 15 points. The descriptions of the presentations are on the Days301
file. I will assign you to your
groups for these presentations randomly, but I want to avoid you having the
same members each time. I expect
each person in a group to contribute to the work; 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 (September
19). 2 - Probability (October
8). 3 - Central Limit Theorem
(November 19). 4 - Statistical
Hypothesis Testing (December 10).
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
Fall 2007 semester are 10:20 to 11:00, Monday, Wednesday, and Friday and 1:50
to 2:50, 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 Days301 file before class.
My
idea of education is definitely not "Teaching is telling and learning is
listening". I believe that
you must be active in the learning process to learn effectively. 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 |
|
September 3 |
September 5 Day 1 |
|
September 10 Day 2 |
September 12 Day 3 |
|
September 17 Day 4 |
September 19 Day 5 |
|
September 24 Day 6 |
September 26 Day 7 |
|
October 1 Day 8 |
October 3 Day 9 |
|
October 8 Day 10 |
October 10 Day 11 |
|
October 15 Day 12 |
October 17 Day 13 |
|
October 22 Day 14 |
October 24 Day 15 |
|
October 29 Day 16 |
October 31 Day 17 |
|
November 5 Day 18 |
November 7 Day 19 |
|
November
12 Day 20 |
November 14 Day 21 |
|
November 19 Day 22 |
November 21 |
|
November 26 Day 23 |
November 28 Day 24 |
|
December 3 Day 25 |
December 5 Day 26 |
|
December 10 Day 27 |
December 12 Day 28 |
Homework
Assignments: (subject to change if
we discover difficulties as we go)
Homework 1, due
September 17
1) The
amount of radiation received at a greenhouse plays an important role in
determining the rate of photosynthesis.
Here are some data on incoming solar radiation. Use both numerical and graphical methods to summarize the data. I don't want to see every method we've used, but I want to see that you know
appropriate summarizing methods.
Briefly explain why your choices were good ones.
6.3 6.4 7.7 8.4 8.5 8.8 8.9 9.0 9.1 10.0 10.1 10.2 10.6 10.6 10.7 10.7 10.8 10.9 11.1 11.2 11.2 11.4 11.9 11.9 12.2 13.1
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 s's 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
September 28
1) If
A and B are independent events with P(A) > P(B), P(AÇB)=.0002
and P(AÈB)=.03,
find P(A) and P(B).
2) Three
married couples have purchased theater tickets and are seated in a row
consisting of just six seats. If
they take their seats in a completely random order, what is the chance that Jim
and Paula (husband and wife) sit in the two seats on the far left? What is the chance that Jim and Paula
sit next to each other?
3) Three
molecules each of four types of molecules are linked together to form a
chain. One such chain is
ABCDABCDABCD; another is BCDDAAABDBCC.
How many such chain molecules are there? What is the chance that a randomly selected chain molecule
has all three molecules of each type adjacent, as in AAADDDCCCBBB?
Homework 3, due
October 5
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) Using
the following cdf, find a) P(X=2)
b) P(X>3) c)
P(2≤X≤5) d)
P(2<X<5)
Homework 4, due
October 22
1) Use
the following pdf and find a) the cdf b) the mean and c) the median of the
distribution.
2) Suppose
grain size in an aluminum/indium alloy can be modeled with the normal curve
with mean 96 and standard deviation 14.
What is the probability that grain size exceeds 100? What is the probability that grain size
is between 50 and 75? What
interval includes the central 90 % of all grain sizes?
3) Suppose
the time it takes for Jed to mow his lawn can be modeled with a gamma
distribution using a=2 and b=.5. What is the chance that it takes at
most 1 hour for Jed to mow his lawn?
At least 2 hours? Between
.5 and 1.5 hours?
Homework 5, due
October 29
1) Here
are the March precipitation values for Minneapolis-St. Paul over a 30 year
period:
.77 1.20 3.00 1.62 2.81 2.48 1.74 .47 3.09 1.31 1.87 .96 .81 1.43 1.51 .32 1.18 1.89 1.20 3.37 2.10 .59 1.35 .90 1.95 2.20 .52 .81 4.75 2.05
Construct
and interpret a normal probability plot for this data. Then take the square root of each value
and construct and interpret a normal probability plot for the transformed
data. Does it seem reasonable to
conclude that the square root of precipitation is normally distributed? Repeat for the cube root.
2) Suppose
that only 20 % of all drivers come to a complete stop at an intersection having
flashing red lights in all directions when no other cars are visible. What is the chance that of 20 randomly
chosen drivers a) at most 6 will come to a complete stop? b) Exactly 6 will? c)
At least 6 will? d) On average, how many of any 20 randomly chosen drivers do
you expect to come to a complete stop?
Homework 6, due
November 5
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
November 26
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
December 3
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) The
desired percentage of SiO2 in a certain type of aluminous cement is
5.5. To test whether the true
average percentage is 5.5, 16 independent samples are analyzed. Suppose the distribution is normal with
standard deviation .3 and the sample mean is 5.25. Does this indicate conclusively that the average percentage
differs from 5.5? Calculate a P-value
and comment on any assumptions you had to make.
Homework 9, due
December 10
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) A
random sample of 539 households from a certain Midwest city was selected, and
it was found that 133 of these households owned at least one firearm. Calculate and interpret a 95 %
confidence interval for the true percentage of households in this city that own
at least one firearm.
3) Forty
percent of a certain population have Type A blood. A random sample of 150 recent donors at a blood bank shows
that 92 had Type A blood. Is there
any reason to think that Type A donors are more or less likely to donate
blood? Use a = .01.
Would your conclusion have changed using a =
.05?
Managed by:
chris edwards
Last updated August 7, 2007