To begin this lesson I show my students a Bounty(TM) commercial and have them select characteristics we can test in the classroom to prove or disprove the product claims in the commercial. My testing 1-2-3 video narrative explains most of this process while this written narrative section provides some additional insights and suggestions. First, be sure that you have materials on hand for this activity including at least two or three brands of paper towels, something to test strength (marbles or pennies work well) and something to test volume of water held (small water bottles and the smallest size dixie cup available, marked on the outside to ensure equal volumes for each test, work well) Second, your students will probably need some help setting up their testing protocols. I find it easiest to work through this as a class to make sure all the data is collected in the same manner. Finally, even if the t-test clearly demonstrates that there is NOT a statistically significant difference, you will probably have at least a few students who will insist that the towel that held more pennies, or water, or whatever you measured is actually better. For those kids I usually come back to the idea that we only ran a few tests on one batch of towels which is kind of like flipping a coin three times and deciding it's unfair if it comes up heads all three times. I remind them that during another series of coin flips we might get tails three times in a row and that another set of tests with the paper towels might have the "losing" brand doing better. I've also included a video of how to use a TI 84 calculator for a t-test.
For this section you will need materials for measuring and at least three brands of paper towels, including Bounty. You will also want copies of the "Additional Data Sets" handout and the"Bounty Dilemma" handout.
Teamwork 15 minutes: I start by distributing the Bounty Dilemma handout and asking my students to read through it and ask any questions they may have. I then have them get all their materials including measuring tools and let them collect data. (MP1) This usually takes about 15 min and during this time I walk around offering encouragement and redirection as needed. As teams finish collecting data I have them post their results on a chart I've created on the board. (You will need to make a row for each measurement you've chosen and a column for each brand of paper towel you are testing) I ask my students that they should each be recording the class data on their papers because they will be working independently for the calculations portion of this activity. I also remind them that they need to return all materials to the appropriate places and clean up their area if necessary.
Independent Practice 10 minutes: When all teams have posted their data I tell my students that they will be working independently for the next section of the lesson and encourage them to finish copying the class data if they haven't already done that. I then tell them to find the mean and standard deviation for each set of data and record it on their paper. Some students will enter the data into a STAT list while others will begin to add all the values in the home screen. (MP5) I have found that those students who are not using the STAT options are generally not comfortable with them and need additional support to be successful with this tool. While it is certainly acceptable to find mean and standard deviation without using a graphing calculator, it is much more time consuming and cumbersome, so I really try to help my students learn when to use this tool as much as how to use it. As they're calculating, I walk around to assist students who need assistance. I also encourage them to answer question 5 on their handout, predicting whether there are any statistically significant differences in the measurements for the different paper towel brands. We've covered significance in an earlier lesson, so this should be review for my students.
Whole Class Instruction 15 minutes: You may want to review the "t-test" video (resource in previous section) before beginning this section. It walks you through using a TI 84 graphing calculator to perform a t-test. I begin this section by telling my students that some of what we are going to do should be familiar to them and some will be new. I encourage them to take notes and ask questions as necessary. I then ask for a volunteer to explain what it means to set a significance level apriori (this is review) and also ask for a suggested level based on what we're testing. (I anticipate that someone will say we should use a 0.05 significance level based on earlier lessons, but if not I make that suggestion myself.) I briefly explain what a t-test is (a comparison of the means of two sets of data for our work) and ask my students if they think a t-test will work for any sets of data we want to compare. This can lead to some interesting discussion and provides me an opportunity to share the limitations/assumptions of using a t-test; that the dependent variable is normally distributed, that sample size is not a factor unless one set is more than 1.5 times greater than the other, and that for our test the variances are assumed to be equal (pooled). I check to make sure everyone is clear on that using fist-to-five then tell my students that they need to enter each set of data into a separate list in their graphing calculator if they have not already done so. (MP5) I ask those who have this task already completed to help their classmates as needed. While they're working I set up my calculator and Document Camera display. You can also do this just by talking, but it's much slower as you stop to help those who get lost. I have included a video of this instruction in my resources as "t-test video". When we've finished running a t-test on one data pair, I ask if there are any questions and tell my students to record the t-value and p-value on their paper, then ask for a volunteer to run the next set with the class. We continue through all the remaining pairs of data with different volunteers for each t-test. When we've finished with all the data, I ask my students to look at the first t-value we found. I explain that it is similar to the z-scores we've worked with and is a measure of spread, but that it doesn't tell us whether or not our means are statistically significantly different. For that we need to look at the p-value. I ask whether the p-value is less than our significance level of 0.05 or not. This is the prize at the end of all their hard work, so I play it up with a bit of drama, whether it's less than 0.05 or not! I ask my students to look at all the other p-values we've calculated and use them to answer question 7 on the handout. (MP1, MP2) There are usually a few students who are still confused about the p-value and significance level so I walk around during this time helping those who need it and/or scheduling extra one-on-one time for them.
To wrap up this lesson I have students briefly summarize when and how to use a t-test and what t-value and p-value mean. This allows them to demonstrate their understanding and to strengthen their ability to communicate precisely (MP6). I use these summaries to help determine who still needs more help with this and what their misconceptions are. Because this lesson pulls together a lot of earlier material, many students have an "ah ha!" moment or two, but some become overwhelmed. I want to reinforce those who get it and support those who need it before moving on, so I write notes to my students on their summary papers and connect one-on-one as needed.