| Students can change the mean or standard deviation and see the effect on the normal curve. Students can click on the plot to verify that the mean is the center of the curve. | |
| Normal Empirical Rule | Define any normal distribution by specifying a mean and a standard deviation. Verify that the area within a certain number of standard deviations of the mean is not affected by the particular choice of parameters. |
Normal Calculator The calculator above takes the place of the traditional textbook table. The calculator can be used in two ways. To find Prob<Z for a Z score, enter a value in the "Area left of" box and hit "Return". The answer is given in red in the "=" box. To find the Z score for a probability, enter a value under in the "=" box and hit "Return". The Z score is given in the "Area left of" box. In each case the graphic provides a visual display of the probability in red. Note that this calculator works for any values of the mean and standard deviation. When thinking in terms of Z scores, you should use 1 as the standard deviation and 0 as the mean. |
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| T Demonstration | By changing the number of degrees of freedom in a t-distribution, students can see how the pdf changes. They also have the option of overlayng the standard normal curve so that they can see the convergence. |
T Calculator The calculator above takes the place of the traditional textbook table. First, enter the appropriate number of degrees of freedom in the top box. Then, the calculator can be used in two ways. To find chi square critical values, enter a probabilitiy in the "=" box and hit "Compute!". The answer is displayed in the "Area right of" box. To Find tail probabilities (or p-values), enter the chi square value in the "Area right of" box and hit "Compute!". The probability will be displayed in the "=" box. In either case, the probability is represented graphically. |
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| Chi-square Demonstration | By changing the number of degrees of freedom in a chi square distribution, students can see how the pdf changes. |
Chi-square Calculator The calculator above takes the place of the traditional textbook table. First, enter the appropriate number of degrees of freedom in the top box. Then, the calculator can be used in two ways. To find chi square critical values, enter a probabilitiy in the "=" box and hit "Compute!". The answer is displayed in the "Area right of" box. To Find tail probabilities (or p-values), enter the chi square value in the "Area right of" box and hit "Compute!". The probability will be displayed in the "=" box. In either case, the probability is represented graphically. |
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| Exponential Demonstration | Students can change the mean and see the effect on the plot of the exponential pdf. Students can click on the plot to see coordinates. |
Exponential Calculator The calculator above allows students to compute probabilities based on exponential distributions. The calculator can be used in two ways. To find Prob > x, enter the value of x in the "Area right of" box and hit "Compute!". The answer is given in the "=" box. To find an x for a probability, enter a value under in the "=" box and hit "Compute!". The x value is given in the "Area right of" box. In each case the graphic provides a visual display of the probability. |
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| Binomial Demonstration | Students can change the binomial parameters n and p and see the effect on a bar plot representing the binomial probabilities. |
| Normal Approximation to the Binomial | Students can change the binomial parameters n and p and see the effect on a bar plot representing the binomial probabilities. The approximating normal distribution (mean np and variance np(1-p)) is overlaid so they can determine when the approximation is good. |
Binomial Calculator The calculator above takes the place of the traditional textbook table. Students should enter the proper binomial parameters (n and p) for the distribution they are interested in calculating probabilities for. Students specify the relevant "x" value and then select among choices such as "exactly", "no more than", etc. Hit "Compute!" to get the answer. The probability is represented graphically in the plot. |
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| Psychic Test | Students can test their "psychic ability" to predict the future by guessing the outcome of a coin toss before it occurs. Enter your predictions by clicking the "heads" or "tails" button. When you enter your guess, the coin is tossed and the result is displayed. As you continue guessing, the applet keeps track of the total number of guesses and the total number of correct guesses, plotting it above. If you are truly psychic, you should be able to beat the odds in the long run. You can "weight" to coin by changing the probability of it landing heads. Are you a psychic? |
| Let's Make a Deal | In a popular game show, contestants are asked to choose one of three doors. Behind one is a fabulous prize! Behind the others are gag gifts. When you choose a door, the game show host shows you a gag gift behind one of the two doors not chosen. You are given the option of switching to the one remaining door or staying with your original choice. Which is the better strategy: switch or stay? You choose doors by clicking on numbers and your chosen door is highlighted. A gag gift (represented by a donkey) is then revealed. Click on the highlighted door to stay, or click on the other door to switch. Then all the doors are opened. Did you win? The table keeps track of your wins and losses using each strategy. |
| Java Applet | Generate a sample from a population and compare the sample mean to the population mean. |
| Java Applet | Generate random samples of n=4 or n=10 |
| Stem and Leaf | transforming a stem-and-leaf display into a histogram |
| Java Applet | taking samples of size 10 from a population of 100 college students |
| Activity 2B | effect of class width on histogram shape |
| Activity 2D | effect of outlier on mean and median |
| Activity 2E | matching means and histograms |
| Activity 2F | matching means and standard deviations with corresponding histograms |
| Activity 3A | scatter diagrams for various correlation coefficients |
| Activity 3B | matching scatter diagrams and correlation coefficients |
| Activity 3C | constructing a scatter diagram for an r = 0.50 |
| Activity 3D | constructing a scatter diagram for an r = -0.90 |
| Activity 5B | calculating binomial probabilities |
| Activity 6A | relationship between probability and area under a normal curve |
| Activity 6B | effect of mean and standard deviation on the normal curve |
| Activity 7A | sampling from a normal population |
| Activity 7B | sampling from a skewed population |
| Activity 7C | sampling American ages from the 2000 census |
| Activity 8A | level of confidence versus width of a confidence interval |
| Activity 8B | estimating the p-value for a one-tailed hypothesis test |
| Activity 8C | estimating the p-value for a two-tailed hypothesis test |
| Activity 9A | exploring the t-distribution for different degrees of freedom |
| Activity 9B | exploring the relationship between a z* value and its corresponding confidence interval |
| Activity 9C | calculating chi square values for various degrees of freedom |
| Activity 10A | exploring the effect of degrees of freedom on the F-distribution |
| Activity 10B | computes probabilities for various F-distributions |
| Activity 13A | explore the relationship between residuals and the line of best fit |