We are happy to announce some new applets at Stats Medic that can help you use simulation to teach inference. Thanks to AP Stats teacher and programmer Bob Amar for making these happen!
Can Joy Smell Parkinson's?
Introducing the logic of significance tests
We use this lesson on the first day of class in order to get students fired up about learning statistics. In an experiment, Joy Milnes was presented with 12 t-shirts -- half of which had been worn by Parkinson's patients and half of which were not. She correctly identified 11 out of the 12 shirts by smell. Was Joy simply guessing or do we have convincing evidence she can smell Parkinson's disease? Have students use this simulation to see what kind of results can happen by simply guessing. This applet can be used by students independently or the teacher can set up a collaborative dotplot using a class code.
Is Mrs. Gallas a Good Free Throw Shooter?
Significance test for a proportion
Mrs. Gallas claims to be an 80% free throw shooter. To prove her skills, she shoots 50 free throws, but only makes 32 shots. Could this result happen purely by chance, or is Mrs. Gallas exaggerating about her free throw skills? To test her claim, we assume she really is an 80% free throw shooter and then investigate what results could happen by chance alone. In the past we have used spinners or random number generators to do the simulation, but now we can actually have Mrs. Gallas shoot free throws! This applet can be used by students independently or the teacher can set up a collaborative dotplot using a class code.
Chi-square goodness of fit test
Candy manufacturers make claims about the distribution of colors for M&Ms and Skittles. In this lesson, we want to collect data to test their claims. Students start with a random sample of M&M’S (or Skittles) from a large bag, enter the observed counts, and then calculate the chi-square statistic. You can then use the applet to simulate random samples from a claimed distribution to see the possible values of the chi-square statistic based on many, many samples. This is a great way to show students that a chi-square distribution is right skewed!
Other New and Updated Applets!
1. Normal distributions (updated): Now displays z-scores, along with areas/boundaries.
2. Law of Large Numbers (new): Watch Mrs. Gallas shoot free throws and see her long-run percentage approach her true percentage. Great for introducing the idea of probability.
3. t distributions (new): Graphs t distributions and does tcdf and Invt calculations. Can also plot a standard normal curve to see how it compares to the t distribution. Start with df = 1 and click the up arrow in the df box to see how the t distributions change (and approach normal) as df increase.
4. χ2 distributions (new): Graphs χ2 distributions and does χ2cdf and invχ2 calculations. Start with df = 1 and click the up arrow in the df box to see how the χ2 distributions change as df increase.
5. Sampling Sunflowers (new): Automates activity from Section 4.1 in The Practice of Statistics (TPS) about stratified sampling. Similar to the Justin Timberlake activity, this activity shows students the benefit of stratified sampling when strata are chosen wisely.