MATH 201 Applied Statistics
Fall 2014
Section 001 8:00 to 9:00 M W
F
Section 002 9:10 to 10:10 M W
F
Instructor: Dr. Chris
Edwards Phone: 424-1358 or 948-3969 Office: Swart 123
Classroom: Swart 101 Text: Introduction to the Practice of Statistics 7th edition,
by David S. Moore and George P. McCabe. Earlier editions
of the text will likely be adequate, but you will have to allow for different
page references. Link to Day
by Day notes
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 will cause
you troubles.
Catalog Description: An introduction to applied
statistics using a statistical computing package such as MINITAB. Topics
include: Descriptive statistics, elementary probability, discrete and
continuous distributions, interval and point estimation, hypothesis testing, regression and correlation. Prerequisite: Mathematics 104 or 108
with a grade of C or better.
Course Objectives: (Click
here for full document.) 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 interest and aptitude in applying statistics to other areas of human inquiry
¥ 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 410 points:
|
Topic |
Points |
Tentative Date |
Exam 1 |
Descriptive Statistics |
93 pts. |
October 6 |
Exam 2 |
Sampling, Probability, and the CLT |
93 pts. |
November 7 |
Exam 3 |
Statistical Inference |
83 pts. |
December 12 |
Group Presentations |
20 Points Each |
60 pts. |
Biweekly |
Homework |
9 Points Each |
81 pts. |
Weekly |
Attendance is a very important component of success in my class because
many of the skills and lessons we will learn will be a direct result of
classroom activities that cannot be reproduced easily. Please attend class as
often as you can. You are responsible for any material you miss. The Day By Day
notes will help you greatly in this regard.
Presentations: There will
be three presentations, each worth 20 points. The descriptions of the presentations
are in the Day By Day Notes. I will assign you to your groups for these
presentations, as 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. Part of your
presentation grade will be based on your own evaluations of how each person
contributed to the presentation. The topics are: 1 – Displays and
Regression (October 3). 2 – Sampling and Probability (November 5). 3
– Statistical Hypothesis Testing (December 10).
Homework:
I will collect several homework problems approximately once
a week. The due dates are listed on the course outline below. While I will only
be grading a few problems, I presume that you will be working on many more than
just the ones 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 donÕt just put down a numerical answer; I
want to see how you did the problem.
(You wonÕt get full credit for just numerical answers.) The method you use and
your description is much more important to me than the final numerical answer. Important Grading Feature: If your
homework percentage is lower than your exam percentage, I will replace your homework percentage with
your exam percentage.
Therefore, your homework percentage cannot be lower than your
exam percentage.
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 2014
semester are 9:10 to 11:00 Tuesday and 3:00 to 4:00 Wednesday, 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 dayÕs 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 not as 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 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.
Monday |
Wednesday |
Friday |
September
1 |
September
3 Day 1 |
September
5 Day 2 |
September
8 Day 3 |
September
10 Day 4 |
September
12 Day 5 |
September
15 Day 6 |
September
17 Day 7 |
September
19 Day 8 |
September
22 Day 9 |
September
24 Day 10 |
September
26 Day 11 |
September
29 Day 12 |
October
1 Day 13 |
October
3 Day 14 |
October
6 Day 15 |
October
8 Day 16 |
October
10 Day 17 |
October
13 Day 18 |
October
15 Day 19 |
October
17 Day 20 |
October
20 Day 21 |
October
22 Day 22 |
October 24
Day 23 |
October
27 Day 24 |
October
29 Day 25 |
October
31 Day26 |
November
3 Day 27 |
November
5 Day 28 |
November
7 Day 29 |
November
10 Day 30 |
November
12 Day 31 |
November
14 Day 32 |
November
17 Day 33 |
November
19 Day 34 |
November
21 Day 35 |
November
24 Day 36 |
November
26 |
November
28 |
December
1 Day 37 |
December
3 Day 38 |
December
5 Day 39 |
December
8 Day 40 |
December
10 Day 41 |
December
12 Day 42 |
Homework
Assignments: (subject to change if
we discover issues as we go)
Homework 1, due September 15
1) The formal
name for garbage is Òmunicipal solid waste.Ó Here is a breakdown of the
materials that made up American municipal solid waste:
Material |
Weight (million tons) |
Percent of total (%) |
Food scraps |
31.7 |
12.5 |
Glass |
13.6 |
5.3 |
Metals |
20.8 |
8.2 |
Paper, paperboard |
83.0 |
32.7 |
Plastics |
30.7 |
12.1 |
Rubber, leather, textiles |
19.4 |
7.6 |
Wood |
14.2 |
5.6 |
Yard trimmings |
32.6 |
12.8 |
Other |
8.2 |
3.2 |
Total |
254.1 |
100.0 |
(Note:
The totals do not add precisely due to individual round-off errors.)
a)
Made a bar graph of the percentages. The graph gives a clearer picture of the main
contributors to garbage if you order the bars from tallest to shortest. Label
your graph, and use a ruler (or software) to make it look professional.
b)
Also make a pie chart of the percentages, either by hand or using software.
Notice that is it easier to see small differences (as in Food scraps, Plastics,
and Yard trimmings) with the bar graph rather than the pie chart. (Observe that
any categorical list can be converted to percentages, and therefore to a
pie chart.)
c)
Comment on which display you prefer for summarizing categorical information.
2) People
with diabetes must monitor and control blood glucose level. The goal is to
maintain Òfasting plasma glucoseÓ between about 90 and 130 mg/dl. Here are the
fasting plasma glucose levels for 18 diabetics enrolled in a diabetes control
class (five months after the end of the class) and for 16 diabetics who were
given individual instruction on diabetes control.
Class
Instruction Group
141 158 112 153 134 95 96 78 148 172 200
271 103 172 359 145 147 255
Individual
Instruction Group
128 195 188 159 227 198 163 164 159 128 283
226 223 221 220 160
Make
a back-to-back stem plot to compare the class and individual instruction
groups. (You will want to trim and also split stems. Remember to include a
definition of your stem unit.) How do the distribution shapes compare? Which
group did better at keeping their glucose levels in the desired range?
3) In
1798 the English scientist Henry Cavendish measured the density of the Earth by
careful work with a torsion balance. The variable recorded was the density of
the Earth as a multiple of the density of water. Here are CavendishÕs 29
measurements.
5.50 5.61 4.88 5.07 5.26 5.55 5.36 5.29 5.58 5.65 5.57
5.53 5.62 5.29 5.44 5.34 5.79 5.10 5.27 5.39 5.42 5.47
5.63 5.34 5.46 5.30 5.75 5.68 5.85
Present
these measurements graphically using either a stem plot, a histogram, or a
quantile plot, and explain the reason for your choice. Then briefly discuss the
main features of the distribution. In particular, what is your estimate (a
single number) of the density of the Earth based on these measurements?
Homework 2, due September 22
1) The
Wade Tract in Thomas County, Georgia, is an old-growth forest of longleaf pine
trees (Pinus palustris) that has
survived in a relatively undisturbed state since before the settlement of the
area by Europeans. A study collected data for 584 of these trees. One of the
variables measured was the diameter at breast height (DBH). This is the
diameter of the tree (in cm) at 4.5 feet above the ground. Here are the
diameters of a random sample of 40 trees with DBH greater than 1.5 cm.
10.5 13.3 26.0 18.3 52.2 9.2 26.1 17.6 40.5 31.8 47.2
11.4 2.7 69.3 44.4 16.9 35.7 5.4 44.2 2.2 4.3 7.8
38.1 2.2 11.4 51.5 4.9 39.7 32.6 51.8 43.6 2.3 44.6
31.5 40.3 22.3 43.3 37.5 29.1 27.9
Find
the five-number summary for these data and the associated box plot. (As usual,
label appropriately.) Also make a histogram and a quantile plot, and compare
the three displays, noting similarities and differences.
2) Different
varieties of the tropical flower Heliconia
are fertilized by different species of hummingbirds. Over time, the lengths of
the flowers and the form of the hummingbirdsÕ beaks have evolved to match each
other. Here are data on the lengths in mm of three varieties of these flowers
on the island of Dominica:
H. bihai
47.12 46.75 46.81 47.12 46.67 47.43 46.44 46.64 48.07 48.34 48.15
50.26 50.12 46.34 46.94 48.36
H. caribaea red
41.90 42.01 41.93 43.09 41.47 41.69 39.78 40.57 39.63 42.18 40.66
37.87 39.16 37.40 38.20 38.07 38.10 37.97 38.79 38.23 38.87 37.78
38.01
H. caribaea yellow
36.78 37.02 36.52 36.11 36.03 35.45 38.13 37.10 35.17 36.82 36.66
35.68 36.03 34.57 34.63
Make
box plots to compare the three distributions. (Use the same scale for each
plot, to make appropriate comparisons.) Report the five-number summaries along
with your graph. What are the most important differences among the three
varieties of flower?
3) High-density
lipoprotein (HDL) is sometimes called the Ògood cholesterolÓ because low values
are associated with a higher risk of heart disease. According to the American
Heart Association, people over the age of 20 years should have at least 40
mg/dl of HDL cholesterol. US women aged 20 and over have a mean HDL of 55 mg/dl
with a standard deviation of 15.5 mg/dl. Assume that the distribution is
Normal.
a)
HDL levels of 40 mg/dl or lower are considered low. What percent of women have
low values of HDL?
b)
HDL levels of 60 mg/dl or higher are believed to protect people from heart
disease. What percent of women have protective levels of HDL?
c)
HDL levels between 40 and 60 mg/dl are considered intermediate, neither very
good nor very bad. What percent of women are in this category?
Homework 3, due September 29
1) How
strong is the relationship between the score of the first exam and the score on
the final exam in an elementary statistics course? Here are data for eight
students from such a course:
First
exam score 153 144 162 149 127 118 158 153
Final exam score 145 140 145 170 145 175 170 160
Which
variable should play the role of explanatory variable in describing this
relationship? Make a scatter plot and describe the relationship in words. Give
some possible reasons why this relationship is not strongly linear.
2) Each
of the following statements contains a blunder. Explain in each case what is
wrong.
a)
ÒThere is a high correlation between the age of American workers and their
occupation.Ó
b)
ÒWe found a high correlation ( = 1.19) between studentsÕ ratings of
faculty teaching and ratings made by other faculty members.Ó
c)
ÒThe correlation between the gender of a group of students and the color of
their cell phone was = 0.23.Ó
3) The
New York City Open Accessible Space Information System Cooperative (OASIS) is
an organization of public and private sector representatives that has developed
an information system designed to enhance the stewardship of open space. Data
from the OASIS Web site for 12 large US cities follow. The variables are
population (in thousands) and open total park or open
space within city limits (in acres).
City |
Population (in thousands) |
Open Acreage |
Baltimore |
651 |
5,091 |
Boston |
589 |
4,865 |
Chicago |
2,896 |
11,645 |
Long
Beach |
462 |
2,887 |
Los
Angeles |
3,695 |
29,801 |
Miami |
362 |
1,329 |
Minneapolis |
383 |
5,694 |
New York |
8,008 |
49,854 |
Oakland |
399 |
3,712 |
Philadelphia |
1,518 |
10,685 |
San
Francisco |
777 |
5,916 |
Washington,
D.C. |
572 |
7,504 |
Make
a scatter plot of the data using population as the explanatory variable and
open space as the response variable. Is it reasonable to fit a straight line to
these data, for either explanatory or predictive purposes? Explain why or why
not. Report the least squares regression equation and superimpose the line on
your graph. Include the value for -squared.
Homework 4, due October 15
1) Explain
what is wrong with each of the following randomization procedures and describe
how you would do the randomization correctly.
a)
Twenty students are to be used to evaluate a new treatment. Ten men are
assigned to receive the treatment and ten women are assigned to be the
controls.
b)
Ten subjects are to be assigned to two treatments, five to each. For each
subject, a coin is tossed. If the coin comes up heads, the subject is assigned
to the first treatment; otherwise they are assigned to the second treatment.
c)
An experiment will assign forty rats to four different treatment conditions.
The rats arrive from the supplier in batches of ten, and the treatment lasts
two weeks. The first batch of ten rats is randomly assigned to one of the four
treatments, and data for these rats are collected. After a one-week break,
another batch of ten rats arrives and is assigned randomly to one of the three
remaining treatments. The process continues until the last batch of rats is
given the treatment that has not been assigned to the three previous batches.
(For purposes of correctly randomizing, assume that you cannot control the fact that there will be four shipments of ten
rats each.)
2) Systematic random samples are often
used to choose a sample of apartments in a large building or dwelling units in
a block at the last stage of a multistage sample. An example will help
illustrate the idea of a systematic sample. Suppose that we must choose four
addresses out of 100. Because 100/4 = 25, we can think of the list as four
lists of 25 addresses. Choose one of the first 25 at random, using your
calculator. The sample contains this address and the addresses 25, 50, and 75
places down the list from it. If Ô13Õ is chosen, for example, then the
systematic random sample consists of the addresses numbered 13, 38, 63, and 88.
A
study of dating among college students wanted a sample of 200 of the 9,000
single male students on campus. The sample consisted of every 45th
name from a list of the 9,000 male students. Explain why the survey chooses
every 45th name. Using your calculator, choose the starting point
for this systematic sample. Be sure to indicate clearly which calculator
command(s) you used.
3) An
opinion poll in California uses random digit dialing to choose telephone
numbers at random. Numbers are selected separately within each California area
code. The size of the sample in each area code is proportional to the
population living there. What is the name for this kind of sampling design?
California area codes, in rough order from north to south are
530 707 916 209 415 925 510 650 408 831 805 559
760 661 818 213 626 323 562 709 310 949 909 858
619
Another
California survey does not call numbers in all area codes, but starts
with an SRS of ten area codes. Using your calculator, choose such an SRS. Be
sure to indicate clearly which calculator command(s) you used.
Homework 5, due October 24
1)
All human blood can be
ÒABO-typedÓ as one of O, A, B, or AB, but the distribution of the types varies
a bit among groups of people. Here are the distributions for the US and
Ireland:
Blood
type |
A |
B |
AB |
O |
US |
0.42 |
0.11 |
0.03 |
0.44 |
Ireland |
0.35 |
0.10 |
0.03 |
0.52 |
Choose
a person at random from each country, independently from one another. What is
the probability that both people have type O blood? What is the probability
that both have the same blood type? (A chart like the one we made for
rolling two dice will help here, but note that the events are not equally
likely.)
2) Internet
sites often vanish or move, so that references to them canÕt be followed. In
fact, 13% of Internet sites referenced in papers in major scientific journals
are lost within two years after publication. If a paper contains seven Internet
references, what is the probability that all seven are still good two years
later? What specific assumptions did you make in order to calculate this probability?
(A probability tree may help understand this calculation, but the
problem can be completed without using a tree.)
3) Non-standard
dice can produce interesting distributions of outcomes. You have two balanced, six-sided
dice. One is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots. The
other die has three faces with 1 spot, 2 faces with 4 spots, and one face with
10 spots. Find the probability distribution for the total number of spots on
the up-faces when you roll these two dice. (A chart like the one we made for
rolling two standard dice will help here, but note that the events are not
equally likely for the second die.)
Homework 6, due October 31
1) Role-playing
games like Dungeons & Dragons use many different types of dice. Suppose
that a four-sided die has faces marked 1, 2, 3, and 4. To determine the
intelligence of your character, you roll this die twice, and add 1 to the
resulting sum of the spots. We assume the faces are equally likely and the two
rolls are independent. What is the average intelligence for such characters?
How spread out are their intelligences, as measured by the standard deviation
of the distribution?
2) Eighty
percent of women at a certain university enroll in the education program, while
twenty percent of men do. Twenty-five percent of the students are females at
this school. What percentage of education majors are women? What percentage of
non-education majors are men?
3) The
scores of high school seniors on the ACT college entrance examination in a
recent year had a mean of 19.2 and a standard deviation of 5.1. The
distribution of scores is not exactly Normal (ACT score is clearly not a
continuous variable) but the Normal curve is a close approximation. (I will
show an example in class.)
a)
What is the approximate probability that a single student, randomly chosen from
all those taking the test, scores 23 or higher?
b)
What is the approximate probability that the mean of 25 randomly chosen
students from among all those taking the test is 23 or higher?
c)
Which of the two calculations above is more accurate? (Note that part a is
really a question from Chapter 1 material.)
Homework 7, due November 19
1) To
assess the accuracy of a laboratory scale, a standard weight known to weight
exactly 10 grams is weighed repeatedly. The scale readings are Normally
distributed with unknown mean (this mean is 10 grams if the scale has no bias,
however). The standard deviation of the scale readings is known (from years of
use) to be 0.0002 grams. The weight is measured five times, with a mean value
of 10.0023 grams. Give a 95% confidence interval for the mean of repeated
measurements of the weight. (Note that the calculator only allows room for 5
digits and a decimal, making this intervalÕs upper and lower values the same.
To conquer this shortcoming of the calculator, consider measuring in
Òmilligrams above 10Ó.)
How
many measurements would have to be taken to get a margin of error of ±0.0001
with 95% confidence?
2) State
the appropriate null hypothesis and alternative hypothesis in each of the
following cases. Make sure you mention a parameter in your answer.
a) A 2008
study reported that 88% of students owned a cell phone. You plan to take an SRS
of college students to see if the percentage has increased.
b) The
examinations in a large freshman chemistry class are scaled after grading so
that the mean score is 75. The professor thinks that students who attend early
morning recitation sections will have a higher mean score than the class as a
whole. Her students this semester can be considered a sample from the
population of all student she might teach, so she compares their mean score
with 75.
c) The
student newspaper at your college recently changed the format of their opinion
page. You take a random sample of students and select those who regularly read
the newspaper. They are asked to indicate their opinions on the changes using a
five-point scale: if the new format is much worse than the
old, if the new format is somewhat worse than
the old, if the new format is about the same as
the old, if the new format is somewhat better than
the old, and if the new format is much better than the
old.
3) One
way to measure whether the trees in the Wade Tract are uniformly distributed is
to examine the average location in the north-south or the east-west direction.
The values range from 0 to 200, so if the trees are uniformly distributed, the
average location should be 100, and any differences in the actual sample would
be due to random chance. The actual sample mean in the north-south direction
for the 584 trees in the tract is 99.74. A theoretical calculation for uniform
distributions (the details are beyond the scope of this course) gives a
standard deviation of 58. Carefully state the null and alternative hypotheses
in terms of the true average north-south location. Test your hypotheses by
reporting your results along with a short summary of your conclusions.
Homework 8, due December 1
1) An
agronomist examines the cellulose content of a variety of alfalfa hay. Suppose
that the cellulose content in the population has a standard deviation of 8
mg/g. A sample of 15 cuttings has mean cellulose content of 145 mg/g.
a)
Give a 90% confidence interval for the true population mean cellulose content.
b)
A previous study claimed that the mean cellulose content was 140 mg/g, but the
agronomist has reason to believe that the mean is higher than that figure.
State the hypotheses and carry out a significance test to see if the new data
support this belief.
c)
What assumptions do you need to make for these statistical procedures to be
valid?
2) Facebook
provides a variety of statistics on their Web site that detail the growth and
popularity of the site. One such statistic is that the average user has 130
friends. Consider the following data, the number of friends in a SRS of thirty
Facebook users from a large university.
99 148 158 126 118 112 103 111 154 85 120
127 137 74 85 104 106 72 119 160 83 110
97 193 96 152 105 119 171 128
a)
Do you think these data come from a Normal distribution? Use a graphical
summary to help make your explanation.
b)
Explain why it is or is not appropriate to use the -procedures
to compute a 95% confidence interval for the true mean number of friends for
Facebook users at this large university.
c)
Find the 95% confidence interval for the true mean number of friends for
Facebook users at this large university.
3) If
we increase our food intake, we generally gain weight. Nutrition scientists can
calculate the amount of weight gain that would be associated with a given
increase in calories. In one study, sixteen non-obese adults, aged 25 to 36
years, were fed 1,000 calories per day in excess of the calories needed to
maintain a stable body weight. The subjects maintained this diet for 8 weeks,
so they consumed a total of 56,000 extra calories. According to theory, 3,500
extra calories will translate into a weight gain of one pound. Therefore, we
expect each of these subjects to gain 56,000/3,500 = 16 pounds. Here are the
weights before and after the 8-week period, expressed in kg.
Subject |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
Weight before: |
55.7 |
54.9 |
59.6 |
62.3 |
74.2 |
75.6 |
70.7 |
53.3 |
Weight after: |
61.7 |
58.8 |
66.0 |
66.2 |
79.0 |
82.3 |
74.3 |
59.3 |
Subject |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
Weight before: |
73.3 |
63.4 |
68.1 |
73.7 |
91.7 |
55.9 |
61.7 |
57.8 |
Weight after: |
79.1 |
66.0 |
73.4 |
76.9 |
93.1 |
63.0 |
68.2 |
60.3 |
a)
For each subject, find the weight gain (or loss) by subtracting the weight
before from the weight after.
b)
Convert the 16 pounds expectation to kg by dividing by the conversion factor of
2.2. Now state the null and alternative hypotheses for this matched pairs test.
c)
Conduct the test and state your conclusions. Include a -value
in your summary.
Homework 9, due December 8
1) Corporate
advertising tries to enhance the image of the corporation. A study compared two
ads from two sources, the Wall Street Journal
and the National Enquirer. Subjects
were asked to pretend that their company was considering a major investment in
Performax, the fictitious sportswear firm in the ads. Each subject was asked to
respond to the question, ÒHow trustworthy was the source in the sportswear
company ad for Performax?Ó on a 7-point scale. Higher values indicated more
trustworthiness. Here is a summary of the data:
Ad
source |
Sample
size |
Mean |
Standard
Deviation |
Wall Street Journal |
66 |
4.77 |
1.50 |
National Enquirer |
61 |
2.43 |
1.64 |
Compare
the two sources using a t-test and
state your conclusions. Include a -value
in your summary. Also include a 95% confidence interval for the true difference
in the trustworthiness for these two sources.
2) The
Pew Research Center recently polled 1,048 US drivers and found that 69% enjoyed
driving their automobiles.
a)
Construct a 95% confidence interval for the true proportion of US drivers who
enjoy driving their automobiles.
b)
In 1991, a Gallup Poll reported this percent to be 79%. Does the Pew data
indicate that the percentage now is different from the 79% figure reported by
Gallup? Perform a -test
and state your conclusions, including a -value
in your summary.
3) A
Pew Internet Project Data Memo presented data comparing adult gamers with teen
gamers with respect to the devices on which they play. The data are from two
surveys. The adult survey had 1,063 games while the teen survey had 1,064
gamers. The memo reports that 54% of adult gamers played on game consoles
(Xbox, PlayStation, Wii, etc.) while 89% of teen gamers played on game
consoles. Test the null hypothesis that the two proportions are equal and state
your conclusions, including a -value
in your summary.
Managed by chris edwards
Last updated July 31, 2014