Math = Love: Statistics: Confidence Interval Projects

Saturday, April 19, 2014

Statistics: Confidence Interval Projects

This year, I had the privilege to teach a non-AP statistics class for high school juniors and seniors who had finished Algebra 2 and were not enrolled in upper level math courses through our local technology center.  As a small high school, our math department offers 10 sections of math: 4 sections of Algebra 1, 3 sections of Geometry, 2 sections of Algebra 2, and 1 section of an advanced math elective.  Last year, the elective was College Algebra.  This year, it is Statistics.  Next year, it will be Trig/Pre-Calculus.  Our local technology center offers Pre-Calculus and AP-Calculus since many of the schools in our area are too small to offer those classes.

I had 5 juniors enrolled in my statistics class this year.  As one of our end-of-year projects, I asked students to ask a question about the population of students (168 students) at Drumright High School.  After getting their questions approved, students had to randomly select 35 students using the random number generator on their calculator and a list of all the students in the school that our school secretary kindly printed off for us.  Next, they found a way to find out how that student would answer their question.

Proof that we are a small school: my students did not have to actually come in contact with all of the students they randomly selected.  For example, one student wanted to know what proportion of DHS students play school-sponsored sports.  After doing his random selection, he could look at the list and instantly know which students were and were not enrolled in athletics.  For those students he was unfamiliar with, a quick question to the rest of the class gave him the information he needed.

The collected data was used to find their p-hat value.  I asked them to make sure the conditions were met to form a confidence interval.  And, I dictated that we would be finding a 95% confidence interval.  If the conditions were met, their task was to find the confidence interval and express their results on a mini-poster.  These posters contain only a summary of their work.  They showed all of their work in detail using the EMCCC model on a separate sheet of notebook paper.

I loved seeing how invested the students were in their projects.  It was great to see them come up with their own questions, generate their own random samples, survey the students, perform the necessary calculations and analysis, and summarize their findings.

This has been my first time ever teaching statistics, so there are definitely a lot of things I would like to change in the future.  But, I'm so glad I got the chance to teach this course this year.  It's been awesome to be able to expose my students to a new field of mathematics!    

Four out of my five students completed the project.  Here are their questions and findings:

What percent of DHS students own an iphone?


What is the proportion of DHS students that have at least one full sibling?


What proportion of DHS students participate in school athletics? 


What percent of DHS students plan on attending college in the near future? 

This one is hard to read because the information was written so small.  

You can be 95% confident that the actual proportion of Drumright students planning to attend college is somewhere between 0.5132 and 0.8268.



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