Below is the outline that I will be following this semester. I will be posting pdf files containing presented material on the class notes web page. Feel free to contact me if you have questions or want any additional information.
Have a great semester!
Inferential
Probability
and
Statistics
UNIT 0 – INTRODUCTION TO STATS
The
first unit covers the opening day. It is designed to build community, give
flavor as to how the course operates, gather information on prior knowledge of
statistics, and provide a glimpse on what statistics is about and what we hope
to accomplish in the course.
- 00-01 Intro
- Discuss syllabus, grading,
policies
- Online textbooks (refer to web
site links), classroom textbook
- Community building
i.
Have
students get in groups of 3 with people they do not know or normally hang out
with
ii.
Have
students share a memorable gift and recent movie they saw
iii.
Students
have 2 minutes and then rotate (do this 3 times)
- Statistics and probability
discussion from activity
i.
How
can we describe quantify these results
ii.
How
representative are these for the class, the school, teenagers in general
iii.
How
many different ways could we form groups of 3
iv.
How
likely would it be for all groups to contain individuals of the same sex,
assuming that there are 12 boys and 15 girls?
- Course survey
- Coin stacking
i.
Ask students to stack pennies as high as
possible using dominant and non-dominant hand
ii.
Record data on data collection sheet
g. Coin
stacking discussion
i.
What are natural questions related to stacking
pennies using dominant and non-dominant hands?
ii.
What do you think the results will show for the
various questions?
1. These
become our hypotheses, our belief or knowledge about what is currently true
iii.
What protocol did you use for penny stacking?
1. Are
protocols consistent?
2. How
does this affect results?
iv.
What was the purpose of this experiment?
1. Assume
want to find out if dominant or non-dominant hand is better at stacking
2. What
if told that the purpose was really to see what percent stacked multiple
pennies at a time?
UNIT
1 – PRODUCING DATA
The
first unit should take approximately 4-5 weeks to complete. Although there are
11 lesson files, several of these, most notably lesson 10, will take more than
one period to complete. Need to weave in simulations as information is
collected. Emphasize what we expect to happen versus what happens: are our data
consistent with expectations? If not, why? Is there something wrong with the
data collected or do we need to adjust our expectations based on the data we
see? On investigations at the end start weaving in data organization and
analysis pieces.
- 01-01 Data Intro
- Look at class survey data
- Consistency
i.
Shoe
size of male versus female
- Missing or erroneous data
- Quantitative versus
categorical data
i.
Define
- Classify data in survey
i.
Is
shoe size categorical or quantitative?
2. 01-02
Experimental components
a. Open
with coin stacking (re-visit or complete if not done previously)
i.
Ask students to stack pennies as high as
possible using dominant and non-dominant hand
ii.
Record data on data collection sheet
b. Coin
stacking discussion
i.
What are natural questions related to stacking
pennies using dominant and non-dominant hands?
ii.
What do you think the results will show for the
various questions?
1. These
become our hypotheses, our belief or knowledge about what is currently true
iii.
What protocol did you use for penny stacking?
1. Are
protocols consistent?
2. How
does this affect results?
iv.
What was the purpose of this experiment?
1. Assume
want to find out if dominant or non-dominant hand is better at stacking
2. What
if told that the purpose was really to see what percent stacked multiple pennies
at a time?
c. Blinding
is when the subject, and possibly the experimenter, of an experiment does not
know the treatment they are being given
i.
Blinding is not required but is desired
1. Single
blind – subject does not know what experimental treatment is
2. Double
blind—both subject and experimenter do not know what experimental treatment is
ii.
Placebo is a treatment that masks whether a
subject is being given a true treatment (think sugar pill)
d. Required
elements of an experiment
i.
Control
1. Compare
two or more treatments
a. What
are treatments and comparisons in penny stacking
2. What
is a control group?
a. Base
to compare against—the status quo, not nothing
ii.
Randomization of assignment into groups
1. How
should randomization be used here?
a. Randomization
of which hand gets used first
iii.
Replication of treatments so have ability to
detect differences
e. What
is the response variable in our experiment?
i.
The variable we wish to measure and understand
f.
What is a factor in our experimental design?
i.
A variable that impacts the response variable
and we want to measure
ii.
Handedness
g. What
are the levels of the factor?
i.
The ways that a factor varies
ii.
Dominant and non-dominant hand
h. What
are treatments?
i.
Combinations of factors
ii.
What if experiment added in blindfold? What are
factors, levels, and treatments?
i.
Cactus example assessment of understanding
j.
Experimental design diagrams
i.
Show generic diagram
ii.
Students create diagram for cactus experiment
iii.
Share and discuss diagrams
k. Could
the strength of dominance impact results in coin stacking? For example, what if
some people are ambidextrous?
i.
What could be done in the experiment’s design to
reduce this impact?
l.
Blocking provides a means to group individuals
with a similar characteristic that may affect results
m. Golf
example
i.
What does a completely randomized design look
like?
ii.
What does a block design look like?
n. Discuss
diagrams
o. How
applicable are the coin stacking results to other groups?
i.
Why or why not applicable to the general
population?
p. What
do we mean by a sample versus a population in statistics?
i.
Population—general group we are interested in
studying or measuring
ii.
Sample—a subset of the population for which we
have gathered information
q. In
coin stacking, who are the population and who are the sample?
r.
What conclusion can we draw from our experiment?
s. How
reliable do you think these conclusions are for the overall population?
i.
The idea of considering the reliability of
conclusions drawn from data is what we mean by inferential statistics
t.
Ethical issues in experimental design
u. Design
an experiment
i.
Discuss designs and ethical issues
3. 01-03
studies
- Characteristics of studies
- Retrospective versus
prospective studies
- Examples
i.
Identify
study type
ii.
Describe
what a study would look like
iii.
Practice
1. Use problem 17 on
page 27 of Elementary Statistics,
Bluman
- Optional video on
observational studies and experiments (Against All Odds?)
- 01-04 Sampling
- Discussion – Desired
characteristics of a sample
i.
Develop
ideas to drive next activity
- Activity – come up with ways
to create a representative sample
i.
Share
out ideas
ii.
Discuss
and name the ideas
- 3 big ideas of sampling
i.
Have
a sample that’s representative
ii.
Randomize
the sample to reduce unanticipated issues
iii.
Sample
size is what matters
- Characteristics of sampling
techniques
i.
Simple
random sample (SRS)
ii.
Stratified
sample
iii.
Cluster
sample
iv.
Systematic
sample
v.
Multistage
sample
viii.
- Assignment
i.
Describe
two of the above sampling techniques applied to AWest students. Cannot use SRS.
- 01-05 SRS and Bias
- Random Rectangles activity
i.
Do
first part – subjective sample versus simple random sample
- Discuss bias and possibilities
in AWest student survey
- How can an SRS be generated
- 01-07 Bias
- Difference between bias and
error
- Generate ideas of how bias
might occur in a survey
- Discuss characteristics of
bias
i.
Volunteer
response bias
ii.
Convenience
sampling
iii.
Undercoverage
iv.
Non-response
bias
v.
Response
bias
- Complete worksheet on random
samples and bias
i.
Use
pages 88-89 in Data Analysis and Probability Workbook
ii.
Have
students sampling technique or bias type
- 01-01A Quiz on studies,
sampling, and experiments
- Mastery Quiz
i.
Definitions
and examples
- 01-10 investigations
- What Do Students Drive?
i.
Activities
and Projects for Introductory Statistics,
page 36-37
ii.
Have
students structure an appropriate sampling technique to use in data collection
(may need to have students look at 2-3 ways of sampling)
iii.
Collect
data and have students organize data
1. Can see what they
know how to do
iv.
Begin weaving in
organizing data lessons (see lesson 02-02 described below)
1. Use contingency
tables, dependence at this juncture.
2. Verify ability to
calculate appropriate percentages from marginal and conditional distributions
3. Verify students can
create segmented bar graphs and interpret results
4. Have students
select an association to investigate (such as vehicle color versus vehicle
type)
a. Create a
contingency table
b. Create a segmented
bar graph
c. Interpret meaning
of results
v.
What follows below
occurs after students have learned probability and simulation
vi.
Have
students make estimates of proportions and simulate results
vii.
Students
collect data and assess if data is consistent with hypothesis
viii.
Students
use binomial model to calculate probabilities of see that number or more (or
fewer)
ix.
Students
modify hypothesis and verify that new hypothesis and data are consistent
x.
Students
write a report as a portfolio problem
1. This will be a
model of what reports should look like
2. Self-developed
mentor text
3.
- What’s In a Name?
i.
Making
Sense of Statistical Studies, pages 48-51
ii.
Use
this to launch into describing distributions
1. Describe shape
2. Why shape is
important
3. Measures of center
and spread
- What Does This Study Do?
i.
Navigating
Through Data Analysis, pages 119-120
- How Fast Do They Melt in Your
Mouth?
i.
Navigating
Through Data Analysis, pages 121-122
ii.
Use
to look at box plots and outliers
1. 5-number summary,
IQR and fences
iii.
Create
hypothesis – what do you think will happen
iv.
Discuss
re-sampling and bootstrapping instead of simulation
- Did You Wash Your Hands?
i.
Making
Sense of Statistical Studies, pages 10-15
ii.
Have
students formulate a question of interest and create a null and alternative
hypothesis
iii.
Students
use the handout questions to discuss how they would proceed with the study.
Students will then carry out the study
- 01-11 Assessment
- Quiz
i.
[optional] Have students read
article and answer questions
1. Marijuana and
obesity
UNIT
2 – ORGANIZING DATA
The
second unit will be covered to ensure students know basic techniques for
displaying and analyzing data distributions. The intent is to support
investigative work. This unit will coincide with the two or three weeks of investigations
that take place at the end of the semester. Although there are 11 lesson files,
several of these, most notably lesson 10, will take more than one period to
complete.
1. 02-02 contingency
tables
a. Show how to create
a contingency table
b. Practice creating
contingency table using class survey data
c. Using contingency
tables to analyze data
d. Practice using
contingency tables
i.
Students
wearing jeans—male vs female
ii.
Eye
color vs hair color
1. Discuss marginal
versus conditional distributions
2. Discuss frequency
versus relative frequency distributions
iii.
School
and smoking worksheet
iv.
Have
students pick an association to investigate from the car data (as explained
under the investigations above)
v.
OPTIONAL: M&M
investigation
1. Is M&M color
independent of hair or eye color of purchaser?
e. Video homework –
calculating relative frequencies
f.
[Only use this to
cover with a substitute.] Investigation
i.
Welcome
to Oostburg, pages 82-86, Making Sense of
Statistical Studies
2. 02-04 graphing
quantitative data
a. What graphs can use
for displaying quantitative data?
i.
Use
to assess prior knowledge
ii.
Help
differentiate between graphs for categorical and quantitative data
iii.
Help
differentiate between graphs for two variables and a single variable
b. Effect of bin size
on histograms
i.
Change
bin sizes for same graph
1. Use name rank data
2. Break into 25, 50 and
100 bins
c. Statistics Through
Applications
i.
Activity
on page 41
ii.
Create
histogram of data
d. Graphs of class
survey quantitative data
e. Discuss how you
would describe the graph
3. 02-05 Shape Center
Spread
a. Shape
i.
Number
of modes
ii.
Symmetric
or skewed
iii.
Gaps,
outliers or unusual features
1. Play outliers video
b. Center
i.
Roughly
where would the center of data falls
c. Spread
i.
How
tightly are data clustered around the center
d. [Optional] Against All Odds Picturing Distributions
Video
i.
http://www.learner.org/resources/series65.html?pop=yes&pid=140#
4. 02-06 Describe
Shape Center Spread
a. Items to address
when describing a graph
b. Symmetry/skewness
example
i.
Then
ask about modes
c. Modes example
i.
Have
students complete description for lower left graph
d. Assessment
5. [optional] 02-07 Quiz on Shape Center Spread
6. 02-08 Center and
Spread
a. Have students
create a histogram of heights using sticky notes
i.
Have
students stand in line from lowest to highest
1. Remove two students
at a time from line, one from each end
2. Continue until have
one or two students standing
3. What do the
remaining students represent?
a. The median!
ii.
Students
write a description of the graph
iii.
Where
do students think the center of the data lies?
b. Calculate the mean
and the median for heights
i.
Which
better characterizes the center of the data distribution?
ii.
What
does the mean measure?
1. Use disks to
demonstrate equal allocation
c. Calculate the mean
and median for name ranks
d. Where is the center
e. Mean versus median
f.
Pick
a center statistic to use
g. Mean affected by
outliers and skewness
h. When to use mean
versus median
i.
Describe
spread of data
i.
Remind
that spread talks about concentration around center of graph
j.
Range
and IQR
k. Range example
l.
Effects
of outliers on range
m. Quartiles
i.
Discuss
how to determine dividing values
n. Finding the IQR
o. Effects of outliers
on IQR
p. 5 number summary
q. 5 number summary
practice
i.
5
number summary practice – Name rank data
ii.
5
number summary practice – Chocolate melting data
r.
[optional] Investigations
from Data Analysis and Probability
Workbook
i.
Average
Temperature, page 37
1. This takes a full
class period
ii.
Wink
Count, page 38
7. 02-11 Box Plots
a. What does a box
plot look like
b. Meaning of box plot
parts
c. 5 steps to create a
box plot
i.
[optional] Watch video on
creating box plot
d. Practice using name
rank and chocolate data
e. Box plots on a
calculator
f.
Side-by-side
box plots
g. Practice – use chocolate melting times by group
8. 02-12 Std Dev
a. Look at plant shrub
heights
i.
How
can we characterize spread around the mean?
ii.
How
far away from the mean is the smallest shrub? What about the tallest shrub?
b. Deviations
c. Mean of deviations
i.
Will
it always be zero
ii.
What
can we do to not make it zero
d. Definition of
variance
i.
No
longer in same units
ii.
What
can we do to put it back into original units
e. Definition of
standard deviation
i.
In
original units
f.
Practice
i.
Calculate
the mean and standard deviation for name rank data
ii.
Calculate
mean and standard deviation for melting times of chocolate types
iii.
Data
set investigations
1. Male and female
heights
g. Effect of
transformations on mean and standard deviation
i.
Discuss
h. Constructing a data
set
9. 02-13 Comparing
Data
a. Comparing two
different graphs of same distribution
b. Comparing
histograms for two different distributions
c. Comparing box plots
d. Things to consider
when comparing distributions discussion
e. Things to consider
when comparing distributions summary
f.
Comparing
distribution video
i.
Against
All Odds Describing Distributions
1. http://www.learner.org/resources/series65.html?pop=yes&pid=140#
g. Investigations
i.
Use
chocolate data to compare melting times
ii.
[optional] Pierre Experiment
1. Pass out slips
randomly
2. Students are not to
discuss or use any outside aid
3. Ask students to write
on post it note
4. Have students write
10 or 100 based upon which slip they received
5. Post on board as
large histogram
6. Mark post it notes
with different colors for 10 and 100
7. Ask students to
describe distribution
8. Next write out
values for each group
9. Ask students if the
number given on the slip affected the estimates
10. Have students do a
comparative analysis and write it up
11. Have students share
out presentations (around 5 or so)
12. Discuss what makes
a good comparative analysis
a. Graphs on same
scale
b. Comparing shape,
center and spread to get overall picture of the distributions
c. Drawing a
conclusion referring to specific values
10. 02-15 z-scores
a. Which
is more unusual?
i.
Discuss as class, how could these be compared?
b. Quick
investigation
i.
Just
reference this from previous work. Only have them perform calculations if don’t
recall results.
ii.
Pick 5 different values
iii.
Calculate the mean and standard deviation
iv.
Now, add a value of 9 to each original value
1. What
happens to mean and standard deviation
v.
Next, subtract a value of 9 from each original
value
1. What
happens to mean and standard deviation
vi.
Multiply each original value by 9
1. What
happens to mean and standard deviation
vii.
Divide each original value by 9
1. What
happens to mean and standard deviation
c. What
will the mean and standard deviation be if you subtract x-bar from each datum
i.
Mean is zero, standard deviation unchanged
1. Instruct
students to try this if they are unsure what will happen
d. What
will the mean be if you divide transformed data by the standard deviation
i.
Mean is zero and standard deviation one
ii.
What are the units of this transformed data
1. Z-scores
are unitless, basically the measure number of standard deviations away from the
mean
iii.
This is known as a z-score
e. What
is the meaning of the z-score
i.
Tells how many standard deviations a value is
away from the mean
f.
Going back to opening question, what if we
calculate the z-score for both items?
i.
Can compare to see which is more unusual
g. Practice
comparing z-scores
i.
Use name rank data, calculate z-scores for min,
max, median, and personal value
1. What
is z-score for mean?
a. Hopefully
students recognize this will be zero
2. Compare
results and discuss any issues
a. Relate
values to standard deviations away from the mean
ii.
Use class survey data and all quant variables
1. Pre-calculate
the mean and std devs for each variable
2. Have
students calculate the z-scores for their individual data
3. Have
students which variable is most unusual for them and which is most normal
iii.
sisters versus shoe size
iv.
cocker spaniels
v.
long jump
h. Work
with z-scores on worksheet
i.
The distribution of z-scores is known as the
standard normal model
i.
Mean is zero and standard deviation is one
j.
Calculate areas under curve
i.
Using table
ii.
Using 68, 95, 99 rule
k. Practice
with normal model worksheet
l.
Transformations
of mean and standard deviation
m. Effect of
subtracting mean from data
n. Effect of dividing
by standard deviation
o. Definition and
properties of a z-score
p. Video
q. Practice
calculating z-scores
i.
Use
average temperature data
ii.
Use
class survey
r.
What
is more unusual
i.
Use
z-scores to compare
s. Standard Score
Worksheet
11. 02-16 Normal Model
a. What does the
distribution of z-scores look like?
b. Distribution is
bell-shaped and is called the standard normal distribution
c. What is the mean of
this distribution?
i.
Students
should recognize that it will be zero
d. What is the
standard deviation of the distribution?
i.
May
say 1 z-score, which corresponds to one standard deviation
ii.
Write
out the sigmas and mean underneath the graph
1. Explain what sigma
and Greek letters represent
e. The area under the
curve totals one
i.
Can
use this to calculate percentages of distribution
f.
Explain
z-table
g. Practice using
z-table
i.
Page
T-1 in Statistics Through Applications
h. What if you are
given the area rather than the z-score
i.
Show
example then practice
i.
How
would you find the area between two z-scores?
i.
Try
to let students come up with way
ii.
If
not, explain can subtract one are from the other
iii.
Practice
this idea
j.
Show
and explain 68-95-99.7 / Empirical Rule
i.
Practice
using the diagram
k. Work on problems on
the worksheet
i.
Additional
practice using Statistics Through
Applications worksheets
1. Sec. 3.2 #1
2. Sec. 3.2 #2
l.
Record
thoughts about how z-scores and normal model can help compare unusual events
12. Mid-term review
self-directed (section 2a)
a. Write down five
most important facts, concepts or topics for this unit
b. Compare lists in
group
c. Record lists on
board and then organize by importance
d. Create a free
response problem for each category of varying degree of difficulty
e. Class answers
created questions
i.
Discuss
choices and question wording
f.
Optional
– re-write questions and choices
g. Work through sample
problems as needed
h. Explain structure
and grading for mid-term
13. Mid-term exam
(section 2a)
Note: The group
project should be introduced at this point in the course!
UNIT
3 – PROBABILITY
This
unit provides basic information on probability, probability models, expected
value, conditional probability and independence. It is designed to provide a
foundation for understanding inference and conducting simulations.
03-01
Probability Rules
·
Probabilities total a value of 1
o
Connect to normal model
o
Give example of heads and tails
o
Ask students for other examples
§
Rolling dice
§
Spinners
§
Deck of cards
§
Marbles in a bag
·
Normal models can represent probabilities
o
Area under curve is 1
o
Rather than ask “what percent of distribution
falls between…”
o
Ask “What is probability that a randomly
selected value falls between…”
§
It’s same evaluation, just a different
perspective on the representation
·
What probability rules do you know?
o
Think, pair, share
o
Run through basic concepts
§
0<=P(A)<=1
§
P(A)=0 means never happens
§
P(A)=1 means always happens
§
P(A) + P(not A) = 1
·
Reference that “not A” is the complement of A
and is sometime written as Ac
03-02
Represent and calculate
·
How can you represent probability situations
o
Ask students then discuss
§
Tables
§
Venn diagrams
o
Use M&M problem
·
Calculating probabilities
o
P(peanut)
o
P(not plain)
o
P(orange and plain)
o
P(orange or plain)
o
P(orange)
·
Reference basic probability rules on page 331
·
Roulette practice
o
P(red)
o
P(even)
o
P(3rd 12)
o
P(1-18 or center column)
o
P(2nd 12 and 3rd column)
o
P(black and even)
o
P(black or even)
o
P(not 19-36)
o
P(0 or 00)
o
P(0 and 00)
o
P(1st spin red and 2nd
spin black)
o
Is the event
“8 and black” mutually exclusive
o
Is the event “25 and black” mutually exclusive
·
Strings
o
Take 3 strings
o
Grab and fold in half
o
Swirl to randomize
o
Tie 2 ends together, do it again, tie last pair
together
o
What are possible outcomes
o
Which do you think most likely to occur, which
least likely to occur
o
Tabulate results and represent
§
Discuss experimental probability versus
theoretical
§
Ask students how three loops could form
·
Step through 3 loop probability, use tree to
help model
·
Compare to experimental result
03-03
conditional and independence
·
Conditional Probability and Independence
o
M&Ms
§
P(orange| peanut)
o
Asthma and smoking
§
Table
§
Venn Diagram
§
Tree
o
Card probabilities
§
Ask for volunteer
§
Choose card from deck; student can win $1 if
guesses drawn card (no suit necessary); student writes guess on slip of paper
which is not shared with anyone
§
Ask class “what is the probability of having a
correct guess?” answer 4/52
§
For a penny give a hint—card is red (or black)
§
“what is the probability of a correct guess?”
answer 2/26
§
For another penny another hint—card is a heart
(or appropriate suit)
§
“what is the probability of a correct guess?”
answer 1/13
§
For another penny give one more hint—card is a
number (or face card)
§
“what is the probability of having a correct
guess?” answer 1/9 or ¼
§
Discuss what information was helpful and what
wasn’t
§
Talk about independence informally
o
Independence
§
Go back through problems to check on
independence
·
M&Ms
·
Roulette
·
Asthma
·
Clothing and gender
o
Bayes
§
P(plain | orange)
§
Asthma
§
Jumping frogs
§
Define general multiplication rule
§
Show how probabilities can be reversed
§
Discuss general concept versus using a formula
§
Use clothing (shorts or jeans, etc depending on
what you see in class) and gender as an example for independence and Bayes
theorem
·
Practice using Chapter 7 Review #2 and “And”
versus “Or” and Independent versus Dependent worksheet
·
Pass out project guidelines
03-04
Birthday problem
·
Counting and probability
o
The Birthday problem
§
Have students record day of birth in month
column
§
Pose question
§
Represent situation for 3 students in a room and
then expand from there
·
Results involve factorials and permutations
03-5
random variables
·
What is a random variable?
o
Variable that depends on chance
·
What is a discrete random variable?
o
Can list out all possible values of variable
·
When make a table and histogram of a variable it
is the probability distribution and probability histogram
o
Use dice roll example
·
What is the mean dice roll?
o
This is called the expected value
o
Calculate expected value for a weighted die
§
Use 1/3, 1/12, 1/12, 1/12, 1/12, 1/3
§
Compare what was done and how they are similar
o
Show formula
§
Calculate another weighted die using 1/3, 1/12,
1/12, 1/3, 1/12, 1/12
§
Connect pieces back to formula
o
Use sibling example to calculate the expected
value
o
What does this value mean?
·
What is the standard deviation of a dice roll?
o
Consider how standard deviation was calculated
before
o
What does this value mean?
·
Use 03-05a Prob Model Mentor texts to establish
what a probability model looks like
o
Point out that the probabilities sum to one and
that if they don’t either a probability is wrong or an outcome is missing
o
Connect back to normal probability and z-table
§
Table is a look at a probability model for
continuous data
·
Coin flipping questions
o
Have students calculate probabilities
§
Create probability model
§
Calculate probabilities
§
Calculate expected value
o
What are characteristics of these problems
§
Two possible outcomes
§
Constant probability
§
Independent trials
§
These are Bernoulli trials
§
Number of successes in fixed trials is binomial
o
How did you go about calculating these
probabilities?
§
Success/failures and number of ways
§
Connect to probability model
§
Discuss how to calculate with a calculator
·
Have students summarize their understanding of
random variables and their connection to probability
·
Practice using Expected Value Worksheet
o
Show how to calculate expected value and
standard deviation using calculator
03-06
Simulating random variables
·
How could a coin toss be simulated using random
numbers?
·
Discuss student ideas about definition of
simulation
·
Show Frayer vocab model
·
Go through terms
o
Provide definition
o
Class discussion of examples
o
Class discussion of non-examples
o
Students use this to complete their own characteristics
·
Terms for Frayer Model
o
Simulation
o
Component
o
Outcomes
o
Trial
o
Response variable
·
Discuss simulation steps
o
Connect to previous knowledge and work
·
Use random number table
o
Use flipping coin example: number of heads in 10
coin tosses
·
Practice using
o
Number of heads in a row when tossing 5 times
o
Number of turns before rolling a sum of five on
two dice
·
Analyzing response variable
o
Practice with one of the practice problems above
·
Practice with worksheets sec7.1 #1 and sec7.1 #1
page 1 and sec7.1 #3 page 2.
o
Worksheet #1 helps solidify digit assignment
o
Worksheet #2 page 1 steps through simulation
process as a model
o
Worksheet #3 page 2 provides practice and allows
assessment of random digit assignment
·
Use expected value worksheet and have students
generate simulations
o
Pull data at tables and then with at least one
other table group
o
Analyze and draw a conclusion about results
·
Exit
o
When setting up a simulation I want to be sure
to ___ because ___
o
The things I am wondering about or have
questions about simulations are ___.
UNIT
4 – INFERENCE
The
fourth unit will be built into the investigations and should take approximately
4 weeks to complete. Formally introduce the idea of null and alternative
hypotheses. Inference will be learned through simulations, re-sampling and
bootstrapping. Simulations were developed extensively in the third unit. The
concepts of re-sampling and bootstrapping will be introduced as methods of
inference for investigations at the end of the third unit. This should be a
more formal look at the idea of inference that has been handled informally
before.
1. 04-01 Big Idea of
Inference
a. Discuss big idea of
inference
i.
Looking
at null versus alternative for question of interest
ii.
Use
chocolate melting experiment for basis
b. What questions can
ask about landmass of the globe
i.
These
are questions of interest
c. Questions of
interest lead to hypothesis statements
i.
Null
hypothesis: what we believe is true
ii.
Alternative
hypothesis: what we are willing to accept if null hypothesis is shown to be
incorrect
iii.
Have
class generate statements for each previously developed question of interest
d. Basics of inference
i.
Question
of interest
ii.
Create
null hypothesis
iii.
Create
alternative hypothesis
iv.
Analyze
situation
e. Writing Hypothesis
Statements Mentor Text
i.
Always,
sometimes, never
f.
Examples
to create null and alternative hypotheses
i.
Baseball
for spring semester
1. If a player consistently gets 4 at bats per game rather than 3 at bats,
will his hitting streak be longer?
2. A player has a 25 game hitting streak. Is his batting average above
.400?
ii.
Football for fall semester
1. If a field goal
kicker averages 4 attempts per game rather than 3 attempts per game, will the
streak of consecutive makes be shorter?
2. Field goal kickers
make attempts from within 40 yards and beyond 40 yards. Are success rates from
beyond 40 yards significantly less?
g. Practice
i.
Create hypotheses for high school sports success
ii.
Page 444, 9.26 and 9.26 in Statistics Through Applications
2. 04-02 Methods of
Inference
a. Revisit the basis
of inference
b. Bootstrapping
i.
How
it works
c. Conducting a
hypothesis test with bootstrapping
i.
How
much of the globe is covered in water?
ii.
Provide
steps
1. Have students
create a hypothesis statement
2. Collect data
3. Simulate results
using software
a. Create a confidence
interval using normal model
4. Have students hand
perform a bootstrap
5. Generate bootstrap
with software
a. Calculate a p-value
i.
Find
z-score (this is the test statistic)
ii.
use
normal model to find probability
6. Draw conclusion
d. Re-sampling
i.
How
it works
ii.
Have
students use determine if more or less water coverage in northern hemisphere
1. Repeat steps of
hypothesis testing with re-sampling
a. Make use of normal
model and z-scores
2. Have students
conduct re-sampling by hand before using software
iii.
Use
data to address hypotheses
1. Land mass in northern
hemisphere versus southern hemisphere
iv.
[optional] This is a good
spot to use the loaded dice
e. Evaluation of
written reports and rubric
i.
Have
students rank works, using rubric as source
ii.
Discuss
what makes a good written report
f.
At
this point, students can work with past data and project data
i.
Project
analysis
ii.
Car
data from earlier sampling activity
iii.
Name
rank data
iv.
Chocolate
melting data
g. [Optional] Use melting
chocolate analysis and results as poster project
h. [Optional] Use hand washing as poster project
3. [do this if
still need help following the analysis and reporting process] 04-03
Investigations from Navigating Through
Data Analysis
a. What Would You
Expect
b. Simulating the Case
c. Analyzing
Simulation Results
d. Recap/Describe
Process Used
e. Simulating and
Counting Success
i.
How
does this relate to previous simulations
4. 04-04 Chocolate
melting – different or same
a. Make a hypothesis—null
and alternative
b. Run simulations
c. Analyze simulations
d. Draw conclusion
5. 04-05 Soda
rankings—same or different
a. Analyze through
resampling
6. 04-06 Name
Rankings—same or different
a. Analyze through
resampling
7. 04-07 Car mileage
a. What would be
unusual?
8. 04-08 Balance time
a. What would be
unusual?
UNIT
5 – EXPLORATIONS IN STATISTICS
Note: The first project
should be rolled out at the end of unit 2. Students will be able to complete
data collection and exploratory data analysis. They will need simulations and
inference techniques to complete the project. Allow students to work in groups
but each student is required to write their own report. One report will be
randomly selected and used as the score for the entire group. All reports will
be examined for originality. If papers are basically copies of each other the
groups’ grade will be lowered one grade.
Time
permitting, a second project (poster project?) could be introduced at the end
of the semester. The fifth unit should take approximately 2 weeks to complete.
Students will apply their knowledge in investigations and projects.
9. 05-01 Project 1
a. By groups
b. Select topic of
interest/question to be answered
c. Design study
i.
Survey,
experiment, or observational study
d. Collect data
e. Analyze data
f.
Run
simulation, bootstrapping, and re-sampling
g. Test inference
h. Draw conclusion
i.
Create
poster
j.
Present
results
10. 05-3 Final Exam
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