# Examples

Initial Publication Date: May 4, 2007

- Coke vs. Pepsi Taste Test: Experiments and Inference about Cause. This activity has students design and carry out an experiment where they try to determine whether or not particular students can correctly identify each cola in a blind taste test. After the experiment is conducted and the data are recorded, a simulation is used to determine whether the experimental results might simply be due to chance, or whether one or more students really can correctly identify the two colas in a blind taste test.
- Reese's Pieces Activity: Sampling from a Population. This activity allows students to construct sampling distributions for samples of Reese's Pieces candies, seeing the effect of sample size on the distributions' shape and developing reasoning about sampling variability. This activity also has students use simulation to determine if a particular result is unlikely or simply due to chance.
- Simulating Size and Power Using a 10-Sided Die: This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves.
- Influence of Outliers on Correlation This activity begins with an instructor demonstration followed by a student out-of-class assignment. Students will observe their instructor create a scatterplot and observe how the correlation coefficient changes when outlier points are added. Students are then given a follow up assignment, which guides them through the applet. In addition, the assignment provides insight about outliers and their effect on correlation. This activity will show exactly how outliers numerically change the correlation coefficient value and to what degree.
- Simulating the Effect of Sample Size on the Sampling Distribution of the Mean: This activity allows students to explore the relationship between sample size and the variability of the sampling distribution of the mean. Students use a Java applet to specify the shape of the "parent" distribution and two sample sizes. The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. Students can see both sampling distributions at the same time making them easy to compare.
- Simulating a P-value for Testing a Correlation with Fathom: Students use simulation to test whether the capacity of major league baseball parks and average attendance at games have a positive association. After creating a plot and finding the correlation for a sample consisting of values for all teams in the 2006 season, students use the Fathom software package to scramble the capacities to see how the sample correlation behaves when there is no association between the variables.
- Using an Applet to Demonstrate Confidence Intervals: Students work individually with an applet to enhance their understanding of confidence intervals. Using a detailed step by step activity, they will use simulated data from the applet to determine the percentage of confidence intervals that capture the population proportion.