Download Integrating the Computer and the Calculator in the Statistics

Integrating the Computer and the
Calculator in the Statistics Classroom
International Conference on Technology in
Collegiate Mathematics
Friday, November 5, 1999
Session: S11
Location: Boardroom IV
8:00 -8:45 AM
San Francisco
11/1/99
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2#
Integrating the Computer and the
Calculator in the Statistics Classroom
Roseanne Hofmann
Montgomery County Community College
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Special Thanks to:
MCCC Foundation
Dean Brad Gottfried
Shayne Clark Wallis
Students who used the materials
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4#
Talking
isn’t
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T
e
a
c
h
i
n
g
5#
Listening
isn’t
Learning
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6#
Research encourages teachers to
Use a Constructivist Approach in Teaching.
Give up the role of “sage on
the stage” to become “guide
on the side.”
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7#
Changes in Teaching Focus
Student
Centered
Teacher
Centered
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8#
Give a fish and they eat
for a day;
teach them to fish and
they eat for a lifetime.
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9#
“Lure” students into
Mathematics by getting
them to “play” with
interesting application
problems.
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10#
Visualization
in the broadest sense has always
been important in mathematics.
Teaching based on visualization requires us
to relearn many of our pedagogical skills.
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11#
Dock and Teach
Borrowing a term from the business
world that uses portable computers
Purpose of Internal Grant
• Use of Notebook Computer in
Classroom, Office, and Home
• Writing of Multimedia modules for
Elementary Algebra
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13#
Bonus
•Use computer for PowerPoint presentations
supplied by Statistics textbook
•Use computer for Statistics CD authored by
Velleman
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14#
Hardware - Obvious
• Projector
• Portable Computer
• Connection to Network
• TI-83 Plus Calculator
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15#
Software
• Velleman CD disk
• Triola PowerPoint Slides
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16#
Cost Concerns
• Software
• Textbook
• Calculator
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17#
Teaching
• Balance of PowerPoint and Velleman CD
• Graphics Calculator
• Group Learning
• Simulations in Class
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18#
MONTGOMERY COUNTY COMMUNITY COLLEGE
Introduction to Statistics I
Fall, 1999
MAT 131 BC 9:05-10:00 a.m.
PH Room 116
MAT 131 CC 10:10-11:05 A.M.
PH Room 116
Roseanne Hofmann, Ed.D.
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CATALOG DESCRIPTION
A basic course designed for students in all fields. Topics include organization of data,
measures of central tendency, measures of variation, statistical inference and correlation.
This is a self-contained course. With MAT 132, it is a course with greater depth and
applications. A graphing calculator is required for class, homework, and testing.
Classroom instruction and programs will be presented using a TI-83+ graphing
calculator.
PREREQUISITES
Math placement test recommendation of “ABV 100” (above MAT 100) or MAT 100,
with a minimum grade of “C”.
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19#
OBJECTIVES/OUTCOMES
Upon completion of this course, students should be able to
1. Understand descriptive statistics by being able to find by hand and using the TI
calculator, mean, median, mode, midrange, range, variance and standard deviation for
a given set of data.
2. Make frequency tables, histograms, frequency polygrams, ogives, pie charts, stem and
leaf plots and box plots.
3. Solve probability problems using the addition and multiplication rules and
complementary events.
4. Understand probability distribution, random variable, mean, variance, and expectation
for the binomial and normal distributions.
5. Understand the normal distribution as an approximation to the binomial distribution
and the Central Limit Theorem.
6. Estimate sample sizes of means and sample sizes of proportions.
7. Test hypotheses: test a claim about a mean, understand p-values, a t-test, and tests of
proportions.
8. Make inferences from two samples using means and proportions.
9. Understand correlation and regression.
10. Understand multinomial experiments and contingency tables.
11. Use the TI graphing calculator to do many of the statistical tests described above.
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20#
REQUIRED MATERIALS
Required Text: Elementary Statistics, 7th edition, Mario F. Triola, Addison-Wesley
Publishing Company, 1998.
1. A TI-83+ graphing calculator
2. ActivStats, CD-ROM, Paul Velleman
SUGGESTED TEXTBOOKS
1. Student’s Solution Manual to accompany the textbook, Milton Loyer
2. TI-83 Companion to Elementary Statistics, 7th edition, Larry Morgan
Student projects will be required.
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21#
TENTATIVE SCHEDULE
September
1 1.1, 1.2; V3.1
3 1.3, 1.4; V8.1
8 2.1, 2.2; V3.2
10 2.3; V4.1
October
November
13 2.4; V4.2
15 2.5; V5.1
17 2.6
October
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20
22
24
27
29
1
2.7; V2.7
Review
Test 1 Chs. 1 and 2
3.1, 3.2 Project Due; V10.1
3.3
3.4; V9.1, 11.1
4
6
8
11
13
15
4.1, 4.2; V13.1
4.3
4.4
Review
Test 2 Chs. 3 and 4
5.1, 5.2; V12.1
18 5.3, 5.4; V14.1
20 5.5
22 5.5
25 7.1, 7.2; V17.1
27 7.3
29 7.3
1 7.4
3 7.5; V19.1
5 Review
8 Test 3 Chs. 5 and 7
10 6.1, 6.2; V15.1
12 6.3; V16.1
15 6.4; V19.1
17 9.1, 9.2; V21.1
19 9.3; V22.1, 23.1
22 10.1, 10.2 Project Due; V24.1
December
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29 10.3
1 8.1, 8.2; V20.1
3 8.3, 8.4
6
8
10
13
Review
Test 4 Chs. 6, 9, 10, 8
Review
Last Class
22#
First Day Data Sheet
Data Sheet
1. _______Sex
2. _______Married/Single
3. _______Height(In)
4. _______Number of Brother and Sisters
5. _______Number of Children
6. _______Birth Month
7. _______Number of Credits currently enrolled for
8. _______Average Number of hours of Sleep per night
9. _______Number of Pierced Ears
10. _______Watch Soaps regularly – yes/no
11. _______Pulse Rate
12. _______Amount of change in pocket or purse
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23#
MAT 131 Fall 1999
Statistics Project (50 points)
PART I Due date: Monday, September 27, 1999
Remember neatness counts and there is a grade reduction for lateness.
1.
(10 pts.) Randomly survey 32 people over 18 years of age. Use either all males or all females.
Obtain the following data for each:
a.
their hand size, measured to the nearest 1/4 inch
b. their shoe size, to the nearest 1/2 inch (Do not include width.)
List the data in the pairs obtained:
i.e. person 1 hand size shoe size
person 2 hand size shoe size
2. (5 pts.) State a purpose for this project. This means you must invent a reason for wanting the
required data. (Use your imagination.) Also state a specific population. (Think about who your
sample represents.)
3. (18 pts.) For the hand size data: find: MEAN, MEDIAN, MODE, RANGE, VARIANCE,
STANDARD DEVIATION, Q1, Q3. Show any work or explain what you did to get your answers.
ALSO, explain what information Q1 gives you in terms of your numbers.
4. (6 pts.) Arrange the hand size data into grouped data. Use 4 or 5 classes. Find: MEAN, MEDIAN,
VARIANCE, STANDARD DEVIATION for this grouped data. Explain what you did or show how
you got your answers.
5. (5 pts.) Compare the common parts of question #3 and #4. What do you conclude?
6. (6 pts.) Arrange the show sizes into a frequency distribution (grouped data) and again use 4 or 5
groups. Make a histogram for this grouped data, carefully labeling each axis with numbers and names.
The histogram should also have a title.
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24#
PART II Due date: Monday, November 22, 1999
For Part II of the project, use the raw data, not the grouped data. Attach a copy of your original data. Then summarize
your data in a table like the following:
HAND SIZE
SHOE SIZE
Sample mean, x
Sample standard deviation, s
Sample size, n
You must show all work (not just answers). If you use your calculator to find an answer, explain carefully what you
did. Again, neatness counts and there is a grade reduction for lateness.
7.
(18 pts.) For the HAND SIZE data:
a.
Give the best point estimate for the average hand size based on your sample results;
b.
Depending on whether your sample was composed of males or females, test the claim that:
AVERAGE HAND SIZE FOR MEN IS 7 1/2
AVERAGE HAND SIZE FOR WOMEN IS 6 1/2
In either case, assume that the population is normally distributed and state your conclusion for  = 0.05.
Give the P-value for the test.
c.
Determine a 98% confidence interval for . Again, assume the population is normally distributed.
8.
(8 pts.) For the SHOE SIZE data:
a.
Determine the best point estimate for the proportion of women with shoe size 6 or of men with shoe size 9,
depending on your sample;
b.
Determine a 99% confidence interval for this point estimate.
9.
(6 pts.) Referring back to the paired data (#1), draw a scatter diagram. Label each axis carefully with names and
numbers. Your scatter diagram should have a title.
10.
11.
12.
(8 pts.) Find "r," explaining how you did it. Determine if there is a linear correlation between shoe sizes and hand
sizes. ( = 0.05)
(8 pts.) Regardless of your answer to the previous question, determine the equation for the regression line and
graph the line on the scatter diagram done in #10. Be sure to give the points you used to graph the line.
(2 pts.) Use the regression line found in #11 to predict the shoe size of a person whose hand size is 6 1/4".
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25#
Mat 131 Jigsaw
Grouping Tool
1. Complete collection of elements to be
studied
2. A subset of a population
3. Numerical measurement describing
some characteristic of a population
4. Numerical measurement describing
some characteristic of a sample
5. Zip code - level of measurement
6. Cars described as subcompact,
compact, intermediate - level of
measurement
7. Temperatures of irate Mat 131 students
over price of book - level of
measurement
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Population
Sample
Parameter
Statistic
Nominal
Ordinal
Interval
26#
Grouping Tool
8. Annual income of doctors - level of
measurement
9. Number of Siblings - discrete or
continuous
10. Heights of Students - discrete or
continuous
11. Equal chance of being selected numbers in hat
12. A sociologist at the CC College
surveys all students from each of 20
randomly selected 4 English Classes
13. A sociologist at the CC College selects
12 men and 12 women from each of 4
English classes
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Ratio
Discrete
Continuous
Random sample
Cluster
Stratified sample
27#
DATA SETS
Given the following data sets find the mean, mode, median, and standard
deviation. Make a table with the data sets in rows and the mean, mode
median, and standard deviation in columns. Draw a box plot and a histogram
for each.
A = 2,3,4,5,6,14,15,16,17,18
B = 2,10,10,10,10,10,10,10,10,18
C= 2,2,2,2,3,16,18,18,18,18
D = 2,3,5,5,6,10,15,18,18,18
E = 2,4,10,10,10,10,10,10,16,18
F = 2,4,8,9,10,10,12,16,18
G = 8,9,9,9,10,10,10,10,11,11,12,13
H = 52,53,55,55,56,60,65,68,68,68
J = 8,8,9,9,9,11,11,11,11,11
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28#
Input the data in L1, L2, L3, etc. Share the list with your partner by having
your partner use GetCalc from the catalogue. Then use One Variable
statistics on each list.
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29#
Source:http://m-ms.com/factory/history/faq1.html
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Hofmann
30#
MAT 131
Multiple Choice Test
Name ____________________________________________
1. The period of time during which reptiles first appeared on earth is the _____ period.
a. Jurassic
d. Cambrian
b. Devonian
e. Lower Cretaceous
c. Triassic
2. The King of England from 1820 to 1830 was
a. George I
b. George II
c. George III
d. George IV
e. George V
3. The chemical element with the atomic number 77 is
a. Iridium
d. Thallium
b. Osmium
e. Rhodium
c. Rhenium
4.
a.
b.
c.
The King of Spain from 1452 to 1516 was
Ferdinand I
Ferdinand II
Ferdinand III
d. Ferdinand IV
e. Ferdinand V
5. The Babylonian cuneiform numeral for 131 is
a. 9    I
b.
 
c. C X X X I
d.   
e.  
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31#
6. The third largest planet in our solar system is
a. Saturn
d. Uranus
b. Earth
e. Neptune
c. Jupiter
7. The 11th president of the United States was
a. Fillmore
d. Tyler
b. Polk
e. Buchanan
c. Pierce
8. The first two men on the moon were Armstrong and Aldrin. On that Apollo flight, who was the third
crew member?
a. Shepard
d. White
b. Schirra
e. Collins
c. Grissom
9. Who recorded the 1979 disco hit “Bad Girls?”
a. Patti LaBelle
d. Gladys Knight
b. Robert Flack
e. none of the above
c. Donna Summers
10. The real name of Lewis Carroll is
a. Charles Lamb
d. Charles Dodgson
b. Charles Brown
e. Charles McCarthy
c. Charles Doyle
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32#
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33#
Triola, page 258:
Given that the population of men has normally distributed weights, with a mean of
173 lb. and a standard deviation of 30 lb., find the probability that if one man is
randomly selected, his weight is greater than 180 lb.
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34#
Triola, page 362
The Jack Wilson Health Club claims in advertisements that “you will lose weight after
two days of the Jack Wilson diet and exercise program.” The Dade County Bureau of
Consumer Affairs conducts a test of that claim by randomly selecting 33 people who
have signed up for the program. It was found that the 33 people lost an average of .37
lb., with a standard deviation of .98 lb. Use a .05 level of significance to test the
advertised claim.
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35#
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36#
Important Distributions
Normal
Uniform
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Skewed Right
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Skewed Left
37#
Notation
S denotes the summation of a set of values
x is the variable usually used to represent the individual
data values
n represents the number of data values in a sample
N represents the number of data values in a population
x is pronounced ‘x-bar’ and denotes the mean of a set of
sample values
µ is pronounced ‘mu’ and denotes the mean of
in a population
all
values
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38#
Definitions
 Mean
the value obtained by adding the scores
and
dividing the total by the number
of scores
S
x
Sample
x =
n
Population
11/1/99
Sx
µ =
N
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39#
Definition
Standard Normal Distribution
• a normal probability distribution that has a
• mean of 0 and a standard deviation of 1
•Area found in
•Table A-2
•Area = 0.3413
•0.4429
-3
-2
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-1
0
1
Score (z )
Figure 5-5
2
3
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0
z = 1.58
Figure 5-6
40#
Figure 5-10
"greater than x"
"at least x"
"more than x"
"not less than x"
Interpreting Area Correctly
Add to
0. 5
Subtract
from
0. 5
0. 5
x
"less than x"
"at most x"
"no more than x"
"not greater than x"
x
Subtract
from
0.5
Add to
0. 5
0.5
x
x
Add
C
Use
A=C–B
A B
"between x1 and x2 "
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x1
x
2
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x1 x 2
41#
7-1
Overview
Definition
Hypothesis
in statistics, is a claim or statement about
a property of a population
Method of Reasoning
Analyze a sample in an attempt to distinguish
between results that can easily occur and
results that are highly unlikely.
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42#
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43#
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44#
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45#
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46#
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47#
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48#
Assessment
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49#
Mat 131 Students Survey – Velleman CD
During this semester, I have asked you to use the Velleman CD. Sometimes I have used
Velleman to demonstrate different topics being discussed in class. Please give your
candid opinion about this CD.
1. Is the Velleman CD helpful?
Explain:
2. Were parts of Velleman(movies, testing, etc.) more helpful than others?
Which? Why?
3. Should I use Velleman next semester?
Explain:
4. If this course were given on-line (no face-to-face instruction – strictly computer)
would you recommend that the students purchase the Velleman CD?
5. Were the powerpoint slides helpful? Explain:
6. Were the powerpoint handouts helpful? Explain:
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50#
RESULTS Mat 131 Students Survey – Velleman CD
1. Is the Velleman CD helpful? Explain:
Yes
12
So-So
5
No
9
2. Were parts of Velleman(movies, testing, etc.) more helpful than others? Which? Why?
3. Should I use Velleman next semester? Explain:
Yes
17
Optional
2
No
9
4. If this course were given on-line (no face-to-face instruction – strictly computer)
would you recommend that the students purchase the Velleman CD?
Yes
23
No
2
5. Were the powerpoint slides helpful? Explain:
Yes
19
So-So
3
No
4
6. Were the powerpoint handouts helpful? Explain:
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51#
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52#
Velleman CD
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53#
Would I do it again?
Yes, for the students.
• Computer animations surpass chalk and
talk
• Sound helped ESL students
• CD allows students to review
• Access for students who missed class
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54#
Would I do it again? Yes, for the teacher.
Would I recommend that you try it? Yes!
• Immediacy
• Flexibility on two levels
• Computer Animations
• Visualization
• Record of material presented
• Computer is another teaching tool
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55#
Q uestions
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56#