I usually save this activity for comparing two means rather than for a single-mean activity. However, this is the one I use:
For reference, an "averaging" die is a special die designed to stay close to the mean. Its faces are 2, 3, 3, 4, 4, 5.
To demonstrate mu1 not equal to mu 2, I created modified averaging dice with the following faces:
Die 1: 3, 4, 4, 5, 5, 6 Die 1 has mu = 4.5 and sigma = .9574
Die 2: 1, 2, 2, 3, 3, 4 Die 2 has mu = 2.5 and sigma = .9574
Randomly assign the class into groups of 3 or 4. Have half of the groups collect and graph data for die 1 while the other half collect and graph data for die 2. Then swap dice and repeat.
Bring the class back together to compare.
With a sample size of 20 rolls on each die, you will have mu1 - mu2 = 2 and an overall spread = .3028, so roughly 98.8% of groups will reject the null hypothesis at the alpha = .05 level.
You can get great dice--in a variety of colors--for this purpose from indentedblankdice.com. Either stick stickered numbers into the indentions or write directly directly on them with a Sharpie. They last forever. :)
Helpfully,Kevin G. Nunn
________________________________ From: Christopher Duran <firstname.lastname@example.org> To: AP Statistics <email@example.com> Sent: Thursday, March 1, 2012 10:50 AM Subject: Re: [ap-stat] Homemade Dice (Inference for Means)
Hello, Has anyone used a "homemade dice" activity to help teach inference for means?
I'm a first year AP Stats teacher. I use BVD and am currently working through Chapter 23.
I'm looking for an activity that can be used to help students understand confidence intervals and hypothesis test for one mean.
I've seen a couple references to a "homemade dice activity," but I'm not sure exactly how I would use homemade dice to illustrate the concepts here.