Confidence Intervals
Project Overview
This RWLO describes a lesson plan that instructs students on how to create a confidence
interval based on the historical snowfall of Chardon, Ohio (41º 34’ 45” North, 81º 12’
16” West). The City of Chardon website includes the historical snowfall (updated
monthly) going back to 1952. The RWLO begins with a review of calculating the mean
and standard deviation using the traditional formulas with a subset of the historical data.
This is followed by using a “short-cut” formula to calculate the standard deviation of the
entire data set and create a confidence interval. By having students work in groups it is
possible to calculate the mean and standard deviations for a variety of 10-year periods
within the data and a confidence interval at different levels. By debriefing at the
beginning of the next class we can use all of this information to show students how only
using part of the data can skew results and how the confidence interval changes when the
level changes.
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Student Learning Objectives
After completing this RWLO students will be able to:
 calculate the mean for a data set using the traditional formula.
 calculate the standard deviation for a data set using the traditional formula.
 calculate the standard deviation for a data set using a “short-cut” formula.
 calculate a confidence interval for a data set.
 describe how using only part of the data set can skew results.
 describe the effect that the level has on the confidence interval.
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Procedure
Time: 50 minutes
Materials: Handouts, pencil/pen, calculator, and computer with Internet access
Background
 This RWLO describes a lesson plan that instructs students on how to create a
confidence interval for the historical snowfall of Chardon, Ohio. Each student
will be assigned to a group for this exercise. The groups will obtain their data for
the exercise as a collaborative unit, but each student will submit their own
completed assignment. The raw data will be downloaded from the City of
Chardon website. Students will be required to calculate the mean and standard
deviation for a specified ten-year period of the historical snowfall data. Each
group then calculates a specified confidence interval based on the entire data set
of historical data. Students will be asked to write a summary of their finding
based on the data analysis.
 This RWLO assumes that students have the prerequisite knowledge required to
calculate the mean, standard deviation, and confidence interval. For lower level
classes the students will need to be given the zα/2 for their confidence interval.
 The Assignment Handout will need to be modified after the 2004 – 2005 year.
Implementation: This RWLO can be used as a classroom exercise or initiated in the
classroom and completed as a homework activity in order to demonstrate the learning
objectives. Each student will be assigned to a group for this exercise. The members of
the group will obtain their data for the exercise as a collaborative unit. Each member of
the group will submit their own completed assignment. The assignment will include the
mean and standard deviation for a specified ten-year period, in addition to a specific
confidence interval and a summary in their own words.
Steps:
 Assemble the students into their assigned groups. Supply each student with the
Assignment Handout and a calculator.
 Describe all necessary information concerning the City of Chardon and provide
the students with its address (http://www.chardon.cc/textdocuments/snow.htm).
 Distribute and review the Assignment Handout.
 Discuss how the class will complete the activity. The entire activity can be
completed in-class if time permits or it can be introduced in-class and completed
as homework. Each group will be given a specified ten-year period and a level
for their confidence interval.
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Provide class time for each group to choose and download a data file from the
City of Chardon website. All groups will use the same data file, but will be given
different ten-year periods and levels for their confidence interval.
This idea could also be used with historical rainfall, high temperatures, low
temperatures, etc. Some changes to the Assignment Handout would need to be
made.
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Content Material
Background: This RWLO describes a lesson plan that instructs students on how to
calculate the mean and standard deviation for a ten-year period of the historical snowfall
of Chardon, Ohio (41º 34’ 45” North, 81º 12’ 16” West). Each student will be assigned
to a group for this exercise. The members of the group will obtain their data for the
exercise as a collaborative unit, but each member of the group will submit their own
completed assignment. The raw data will be downloaded from a website created by the
City of Chardon. Students will be required to calculate the mean and standard deviation
for a specified ten-year period within the historical snowfall data, then calculate a
specified confidence interval using the entire data set. At the end of the assignment
students will be asked for a brief summary of their confidence interval.
Student Directions
 Assemble into your group at a computer connected to the Internet and access the
City of Chardon website at (http://www.chardon.cc/textdocuments/snow.htm).
 Once your group has found the data file, send enough copies to the printer so
every group member has one.
 Read the Assignment Handout provided by your instructor.
 Obtain a Calculator from the instructor if it hasn’t been provided.
 Complete the assignment.
Additional Resources
 The historical snowfall data for Chardon, Ohio has been downloaded into an
Excel file within my RWLO folder.
 The historical snowfall data for Chardon, Ohio has been downloaded into PDF
files within my RWLO folder.
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Assessment
Each of the sections of the Assignment Handout can be used for assessment based on the
following rubric:
Mike’s Result: [5 total points]
 Calculate the mean and standard deviation for a ten-year period of snowfall
data.
Mike’s result will be scored as follows:
5 pts = All of the requirements listed below have been fulfilled.
a) Complete the top part of the table correctly on page 2 of the Assignment
Handout.
b) Complete the sums of columns 2, 3, and 4 of the table correctly on page 2.
c) Calculate the correct mean for the ten-year period.
d) Calculate the correct standard deviation for the ten-year period.
e) Summarize the results correctly in step 9.
4 pts = Four of the five requirements have been fulfilled.
3 pts = Three of the five requirements have been fulfilled.
2 pts = Two of the five requirements have been fulfilled.
1 pts = One of the five requirements has been fulfilled.
0 pts = None of the requirements have been fulfilled.
Kelley’s Result: [8 total points]
 Calculate the mean, standard deviation, and confidence interval for the entire
snowfall data set.
Kelley’s result will be scored as:
8 pts = All of the requirements listed below have been included.
a) Complete the top part of the table correctly on page 4 of the Assignment Handout.
b) Complete the sums of columns 2 and 3 of the table correctly on page 4.
c) Calculate the correct mean for the entire data set.
d) Calculate the correct standard deviation for the entire data set.
e) Calculate the correct zα/2 for the entire data set.
f) Calculate the correct lower bound for the confidence interval.
g) Calculate the correct upper bound for the confidence interval.
h) Summarize the results correctly in step 10.
Each missing requirement results in the loss of one point.
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Summary: [7 total points]
 Briefly summarize this assignment.
 What does Kelley’s confidence interval tell us?
 How does Mike’s results compare to Kelley’s results?
 What surprised you?
The summary will be scored as:
7 pts = All of the requirements listed below have been fulfilled.
a) Brief summary of the assignment.
b) Correct interruption of Kelley’s result. (2 points)
c) Correct comparison between Kelley’s result and Mike’s result. (2 points)
d) Describe at least one surprise that occurred during this assignment.
e) Completed on time.
Each missing requirement results in the loss of corresponding points (one, if not listed).
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Links to Course Competencies
This RWLO can be used in a variety of mathematics courses. The RWLO is best suited
for courses in probability and statistics. Upon completion of this RWLO the following
list of competencies shall be met.
 Students will be able to find the measures of central tendency and dispersion
for a set of observations.
 Students will be able to demonstrate an understanding of the normal
distribution and use the standard normal table.
 Students will be able to demonstrate an understanding of inferential statistic.
 Students will be able to solve applied problems using the standard normal
table.
 Students will be able to demonstrate the use of a computer and the Internet.
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Supplementary Resources
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Australian Annual Mean Rainfall, Yearly Australian rainfall from 1900
through 2002 (http://www.bom.gov.au/climate/change/rain03.txt)
Total Seasonal Rainfall 1877 – Present, Yearly rainfall at the Los Angles
Civic Center from 1877 through 2005
(http://www.laalmanac.com/weather/we13.htm)
Historical Temperature Summaries for Central Wisconsin, Monthly
average temperatures of Central Wisconsin from 1895 through 2004
(http://www.aos.wisc.edu/~sco/divisions/4705-T.html)
Glossary of Statistical Terms
(http://www.stat.berkeley.edu/~stark/SticiGui/Text/gloss.htm)
Statistical Glossary – Confidence Intervals
(http://www.cas.lancs.ac.uk/glossary_v1.1/confint.html)
Table of the Standard Normal (z) Distribution
(http://www.isixsigma.com/library/content/zdistribution.asp)
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Recommendations
Implementation:
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This RWLO can be used in various mathematics courses to demonstrate the
importance of confidence intervals. The design of the RWLO requires students to
work cooperatively in a group to identify and download the data file which each
student will use independent of the other group members, to complete the RWLO.
Use approximately 5 minutes to describe the activity.
Print out all the required materials references in the content material section of
this RWLO. This includes the Assignment Handout and the website (if Internet
access is not available).
Back up:
 If the primary website for the City of Chardon is unavailable, the historical
snowfall data for Chardon, Ohio has been downloaded into Excel and PDF files
within my RWLO folder.
As a precaution, print at least one copy of a data file from the City of Chardon website in
case the Internet becomes inaccessible.
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