Gives some background on the Buffon needle problem. Has a link to an applet that allows one to simulate dropping a needle1, 10, 100, or 1000 times. One also has control over the length of the needle.
Poses the following problem: Suppose there was one of six prizes inside your favorite box of cereal. Perhaps it's a pen, a plastic movie character, or a picture card. How many boxes of cereal would you expect to have to buy, to get all six prizes?
An applet explores the following problem: A long day hiking through the Grand Canyon has discombobulated this tourist. Unsure of which way he is randomly stumbling, 1/3 of his steps are towards the edge of the cliff, while 2/3 of his steps are towards safety. From where he stands, one step forward will send him tumbling down. What is the probability that he can escape unharmed?
This applet is designed to approximate the value of Pi. It accomplishes this purpose by firing random data points at a circle inscribed within a square. The probability of a data point landing within the circle is a ratio of the circle's area to the area of the square.
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. Key words: Power, size, hypothesis testing, binomial distribution
This group activity focuses on conducting an experiment to determine which of two brands of paper towels are more absorbent by measuring the amount of water absorbed. A two-sample t-test can be used to analyze the data, or simple graphics and descriptive statistics can be used as an exploratory analysis. Students are asked to think about design issues, and to write a short report stating their results and conclusions, along with an evaluation of the experimental design. Key words: Two-sample t-test