1. Jimmy Clemson
Dr. Adu-Gyamfi
MATE 4001
11/3/13
Artifact 1
Every summer I go to amusement parks to ride rollercoasters. I try to get to new places
all the time to experience new rides but each time I go to a new amusement park I never know
which coaster to go to first. I need to find some way to narrow down the options a little so the
decision becomes a little bit easier. So should I go to a wooden coaster or a steel coaster first?
Question: What are the statistically significant differences between wood roller coasters
and steelroller coasters?Take p<.05 to determine significance.
To start looking at this question I first took the category of largest drop. I created a graph that
displayed the largest drops of steel tracks versus wooden tracks. While the steel tracks have

2. higher values, it also has much more variability. The mean of the steel is 193.5 while the wood
was 132.7. The test statistic is 1.398. The probability for a test statistic of t=1.398 is .19. Since
.19>.05 this is not a statistically significant difference between the two populations. Even when
only looking that
yields a p value of .09 which is still not a significant result.
From there I went to test the differences in the heights of the coasters. The story of this category
is much the same as the last one. The steel coasters have a higher mean and much more
variability than the wooden coasters. The means are, steel=194.125, wood=132.571. The
standard deviations are steel=105.292 and wood=51.7232. With a t value of 1.464 and a
corresponding p value of .17, this is also not a statistically significant difference between the
wood and the steel coasters. Next I will test the length.

3. Looking at the length of the coasters now, we can see that the means of the two distributions are
very similar with the steel coasters once again having the most variability. The means and
standard deviations are as follows: mean of steel is 4527.62, mean of wooden is 4380, standard
deviation of steel is 2333.97, standard deviation of wood is 1565.02. With a t value of 0.1454
these two distributions are extremely similar. This corresponds to a p value of .89 which is
definitely not statistically significant. So far I have not found one category that is statistically
significant between steel and wooden coasters. Next I will look at top speed.

4. Here we have two distributions where the steel is more varied than the wooden coasters and also
has a higher mean than the wooden. In this one there is one particular outlier that is really
skewing the steel data. The means and standard deviations are as follows, mean for steel is 69
and for the wood is 59.9, the standard deviation for the steel is 27.7 and for the wood is 12.58.
The test statistic is .831 which corresponds to a p value of .43. Now we have looked through
each of the attributes and there are not any that are statistically significant. I wonder if the
outlier in this last case is skewing the data too far, so I am going to see if that is the case.

5. After having deleted the outlier which was named Cobra and was a family ride which seemed to
be skewing the data, we have some new information. The mean and standard deviation of the
wooden tracks are the same but the standard deviation and mean for the steel tracks are slightly
different now. The mean is now 76.2857 and the standard deviation is now 20.0559. With these
new measures we now have a test statistic of 1.826 which corresponds to a p value of .097. By
taking out the one outlier we have shown there is more of a difference in their distributions than
thought was there with the outlier even though this still doesn’t qualify as statistically significant
if we use the defined significance above.

6. IDP TPACK TEMPLATE (INSTRUCTIONAL DESIGN PROJECT TEMPLATE)
NAME: ______Jimmy Clemson______ DATE:________11/4/13________
Content.
Describe: content here.
(COMMON CORE STANDARDS)
CCSS.Math.Content.HSS-IC.B.5 Use data from a randomized
experiment to compare two treatments; use simulations to decide
if differences between parameters are significant.
Describe:Standards of mathematical Practice
CCSS.Math.Practice.MP1 Make sense of problems and persevere
in solving them.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP3 Construct viable arguments and
critique the reasoning of others.
CCSS.Math.Practice.MP5 Use appropriate tools strategically.
CCSS.Math.Practice.MP6 Attend to precision.
Pedagogy. Pedagogy includes both
what the teacher does and what the
student does. It includes where, what,
and how learning takes place. It is about
what works best for a particular content
with the needs of the learner.
1. Describe instructional strategy (method) appropriate for the content, the learning
environment, and students. This is what the teacher will plan and implement.
This will be an exploratory lesson. The students will already have learned what
hypothesis testing is and have been introduced to a two sample t-test. I will review this
at the beginning of the period and then introduce the data. From here I would ask the
students about different roller coasters they have been on and their experiences on
them. After each response I will try to find out what kind of coaster it was and then
pose the question are there any significant differences between the wooden and steel
coasters.
2. Describe what learner will be able to do, say, write, calculate, or solve as the
learning objective. This is what the student does.
From there the student will explore whether there are any significant differences
between the two. They will soon find out that there are no statistically significant
differences.
3. Describe how creative thinking--or, critical thinking, --or innovative problem
solving is reflected in the content.
For the most part what the students have done so far will not have involved too much
critical thinking. They so far have just had to know how to do a significance test and
understand what each of the values produced means in context.

7. Once the students see that none of the ones are significant, I will prompt them to think
about why that is even though there seems to be quite a discrepancy between the
distributions. I will have the students write up why they think it is that there wasn’t
any significant difference and have them turn it in.
Technology.
1. Describethe technology
The technology used was Fathom. Fathom is a micro world technology that
focuses in the use of statistics. It allows easy use of graphs and tests involved in
inferential statistics.
2.
Describe how the technology enhances the lesson, transforms content, and/or
supports pedagogy.
The technology allows the students to see a graph of each of the categories with wood
versus steel. By seeing this they can see that there is discrepancies between the two
distributions and it is reasonable to test if they are different or not. By doing the
significance tests on fathom as opposed to a calculator or another program allows the
students to more easily test for significance without have to input everything into lists,
since the lists are already made out. This way they can spend the bulk of their time
trying to figure out why stuff is the way it is opposed to spending the bulk of their time
inputting data.
3. Describe how the technology affects student’s thinking processes.
Thestudent will see the graphs of each and think that there might be a significant
difference between the two tracks. Hopefully this leads them to question why
there is not a difference try to figure that out.
Reflect—how did the lesson activity
fit the content? How did the technology
enhance both the content and the lesson
activity?
Reflection

8. Lesson Plan Template MATE 4001 (2013)
Title: Is there a significant difference between wooden and steel roller coasters
Subject Area: Statistics
Grade Level: High School
Concept/Topic to teach: Testing for the significance between two means
Learning Objectives:
Content objectives (students will be able to……….)
Students should be able to figure out if there are any significant differences between wooden and steel
roller coasters and understand why there is not even though there appears to be a large difference in
some of their distributions.
Essential Question
What question should student be able to answer as a result of completing this lesson?
Is there a significant difference between wooden and steel roller coasters? Also what factors
contribute to the fact that there isn’t any significant difference although it seems there is a difference
in the distributions.
Standards addressed:
Common Core State Mathematics Standards:
CCSS.Math.Content.HSS-IC.B.5 Use data from a randomizedexperiment to compare two
treatments; use simulations to decide if differences between parameters are significant.
Common Core State Mathematical Practice Standards:

9. CCSS.Math.Practice.MP1 Make sense of problems and perseverein solving them.
CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.
CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.
CCSS.Math.Practice.MP5 Use appropriate tools strategically.
CCSS.Math.Practice.MP6 Attend to precision.
Technology Standards: Copy and paste from NCDPI
HS.TT.1.1
Use appropriate technology tools and other resources to access information
(multi-database search engines, online primary resources, virtual interviews
with content experts).
HS.TT.1.2
Use appropriate technology tools and other resources to organize information
(e.g. online note-taking tools, collaborative wikis).
Required Materials:
List all materials needed for your lesson
Computers
Fathom
Notes to the reader:
Students should already have been introduced to a significance test.
Time: Assume 60 minutes ***
Time
Teacher Actions
Student Engagement
Introduction
I will review how totake a significance
test on Fathom at the beginning of the
period and then introduce the data.
From here I would ask the students
about different roller coasters they
have been on and their experiences on
them and which their favorite is. After
Students will be answering general
questions on roller coasters, like which
their favorite is and details about
them, specifically wood and steel.
5-10

10. each response I will try to find out
what kind of coaster it was and then
pose the question are there any
significant differences between the
wooden and steel coasters.
Tell them that they have access to data
on certain roller coasters and that I
want them to answer my question.
They are to create a graph of the data
and perform the hypothesis test.
Investigation Circulate the room to see how
everyone is doing. Answer questions if
30
need be. Ask questions to figure out
their thoughts.
Small Group
discussion
5 min
Large group
discussion
10
Students will be creating graphs of
each category with steel vs. wood and
performing significance tests of the
data. They will be interpreting their
results to determine significance.
Pair up and share their thoughts on the Students will discuss their
data that they just analyzed. Have
observations.
them focus on what their results were
and why they think they obtained
those results.
“What were the significant differences
between the wood and steel
coasters?”
None
“Type up why you think that is to turn
in. And what could be done to get a
result with less of a standard error?”
Too small of a sample/need a
larger sample
Outliers mainly in the steel
category considerably reduced
the means of the steel coasters
and raised the standard
deviation, leading to a much
Students will type up their responses
to the posed question to turn in.

11. smaller test statistic.
*** Your lesson plan should ALL be included here (the reader shouldn’t have to go anywhere else to find
the plans.) The teacher should be able to read it chronologically. The only things to be included at the
end of the plan are supplemental artifacts (e.g. handouts, tech files, ppt). If you chose not to use the
table then the time, teacher actions and student actions should be clearly noted throughout your plan.
Make sure that your lesson is detailed enough that someone else could teach from it. This is
especially important during class discussion phases. For example, be sure to detail what the
teacher should be sure to bring out in a whole class discussion, including questions to push
students to build conceptual understanding, questions to assess student understanding, and
transitions between portions of your lesson.
If students are working in pairs / small groups this should be noted (including how the groups
are to be determined)
All tasks / examples should be worked out and included in the body of the lesson plan
All HW should be worked out
Reflection
Going through this lesson on Fathom I found it very easy to perform the tasks that were
presented. It was very easy to graph each category and display each as a scatterplot and also to
perform the hypothesis test. The ease at which you can do that allows the students more time to
try and interpret both the graph and the results. The one drawback I found was that when I read
through the hypothesis test, there is so much information presented in a small area that I felt
overwhelmed and it took me a couple minutes to sift through everything that had been given and
figuring out everything and what it meant. For the students it gets rid of the tediousness of
finding/entering all the data and allows them more time to work on the inferential part of
statistics (which is what statisticians get paid to do). The only drawback is that in having
everything instantly, students could lose the meaning behind each of the statistics that are
brought up and how concepts are interrelated and affect each other.