Probability

  • This activity is an advanced version of the "Keep your eyes on the ball" activity by Bereska, et al. (1999). Students should gain experience with differentiating between independent and dependent variables, using linear regression to describe the relationship between these variables, and drawing inference about the parameters of the population regression line. Each group of students collects data on the rebound heights of a ball dropped multiple times from each of several different heights. By plotting the data, students quickly recognize the linear relationship. After obtaining the least squares estimate of the population regression line, students can set confidence intervals or test hypotheses on the parameters. Predictions of rebound length can be made for new values of the drop height as well. Data from different groups can be used to test for equality of the intercepts and slopes. By focusing on a particular drop height and multiple types of balls, one can also introduce the concept of analysis of variance. Key words: Linear regression, independent variable, dependent variables, analysis of variance

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  • An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination. Key words: Probability distribution, binomial distribution, computer simulation, decision rules
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  • Residual plots and other diagnostics are important to deciding whether or not linear regression is appropriate for a set of data. Many students might believe that if the correlation coefficient is strong enough, these diagnostic checks are not important. The data set included in this activity was created to lure students into a situation that looks on the surface to be appropriate for the use of linear regression but is instead based (loosely) on a quadratic function. Key words: regression, residuals
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  • A TI graphing calculator emulator. Emulates the TI-82, TI-83, TI-83 Plus, TI-85, TI-86, TI-89, TI-92, TI-92 II, and TI-92 Plus. Features a graphical debugger, grayscale, send/receive, black-link, parallel link and more. User must transfer calculator's ROM to the computer through TI-Graph Link.

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  • 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

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  • A mathematical word processor that includes an easy-to-use computer algebra system (MuPad). Products include Scientific Wokplace, Scientific Word, Scientific Notebook, and MuPad Pro. Student version are available.

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  • The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the "variation" in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation. Key words: Variability, standard deviation

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  • 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

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  • The Food and Drug Administration requires pharmaceutical companies to establish a shelf life for all new drug products through a stability analysis. This is done to ensure the quality of the drug taken by an individual is within established levels. The purpose of this out-of-class project or in-class example is to determine the shelf life of a new drug. This is done through using simple linear regression models and correctly interpreting confidence and prediction intervals. An Excel spreadsheet and SAS program are given to help perform the analysis. Key words: prediction interval, confidence interval, stability

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  • The program DistCalc calculates probabilities and critical values for the most important distributions. The purpose of this program is to show the concept of critical values and the replacement of printed distribution tables. The Distribution Calculator offers calculations for the normal distribution, the t distribution, the chi-square distribution, and the F distribution.

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