# Continuous

• ### Analysis Tool: Binomial Distribution Applet

This applet simulates drawing samples from a binomial distribution. Users set the population proportion of success (pi), sample size (n), and number of samples. By clicking "Draw Samples," the applet will draw a sample and display the corresponding sample histogram. Each new sample drawn is added to the previous ones unless the user clicks "Reset" between samples. Users can choose to display the number and proportion of successes above or below a certain value (tail probabilities) by entering a value in the "Num Successes" box and clicking "Count." The portion of the distribution that meets the condition is highlighted in red, and the proportion of success is given at the bottom of the page. Clicking the inequality sign changes its direction. Clicking "Theo Values" displays the theoretical distribution in green on top of the empirical. Instructions and an activity for this applet can be found in the textbook "Investigating Statistical Concepts, Applications, and Methods" (ISCAM) in Lesson 3.2.2 on page 205.

• ### **Interactive Games

This applet allows users to play several probability games like Monty Hall, Gambler's Ruin, Galton's Board, etc. Select a game from the drop down menu and click "About" to read its background. Users can manipulate the parameters for each game. Graphs of the theoretical and empirical distributions are shown. Requires JAVA.
• ### Histogram Applet

This applet generates a histogram for two provided datasets, or by clicking "Edit Data", users can input their own data. Users can also manipulate the axes and bin width.
• ### **Dotplot Summaries Applet

This applet generates dotplots for different data sets and allows users to guess the location of various measures of center and spread. Clicking "Resample" produces a dotplot of random data generated by the applet. A dotplot of user-input data can be generated by clicking "Edit Data" and typing or copy and pasting the data in the textbox. To guess the mean, median, standard deviation, and interquartile range (IQR) users check the "Guess Mean/Median", "Guess Deviation", or "Guess IQR" box and slide the relevant marker along the horizontal axis. When "Guess Deviation" is selected, users can also select "Show Percentages" to display the percentage of data points within the user's current guess for standard deviation. Clicking "Show Actual" displays the actual position of the selected measure on the dotplot. Clicking on an individual data point shows its value. Users can edit the data under "Edit Data" or by clicking and dragging the data points on the graph.
• ### Least Squares Regression Applet

This applet shows a scatterplot of height versus foot length. Users can add or delete points and then guess the regression line by clicking "Your Line" and moving the blue regression line. By clicking "Regression Line" users can see the actual regression line. The applet also shows the correlation and R-square for the data as well as the residuals and squared residuals for the guessed regression line and the actual regression line.
• ### Normal Probability Calculator

This applet allows users to calculate probabilities from a normal distribution. First, set the mean and standard deviation and click "Scale to Fit". Check one of the boxes next to the inequality signs and enter a value for x; the applet will calculate the z-score and cumulative probability (shown in dark blue for top value and pink for the bottom). By clicking both boxes, users can see the probability between two values (in pink) or outside two values (in blue). Click the inequality sign to change the direction of the cumulative probability.
• ### Power Simulation JAVA Applet

This applet demonstrates the concept of power. Users select the hypothesized mean, the alternative mean, the sample size, and the number of samples. The applet shows the hypothesized histogram and the alternative histogram. Users then select either the level of significance and set alpha or the rejection region and set the test statistic. The applet then shows the p-value (in red) and power (in green). User can also determine the direction of the test by clicking the inequality sign.

• ### Dataset: Exploratory Teratology Study in Rats

This dataset comes from a study on pregnant rats. Forty rats were given 4 doses of a drug, and data on their fetuses were collected. Questions this study focused on refer to the relationship between dosage of the drug and gender of the fetus. A text file version of the data is found in the relation link.
• ### IDEAL: The Normal Distribution

This module discusses the history and importance of the normal distribution, as well as normal moments, the standard normal distribution, normal probabilities, Z-Scores, and normal quantiles. The applet allows users to compute normal probabilities and quantiles. Three follow-up examples cover cholesterol, male heights, and mean temperatures for various cities in South Carolina.
• ### Dataset: Swim Maze Testing in Rat Pups

This dataset comes from a study on rats swimming in a T-shaped maze. Rats were given 4 doses of a drug, and their resulting pups swam the maze until they successfully escaped it 3 consecutive times. Questions from this study refer to the dosage of the drug, the number of swims until 3 consecutive successful escapes, and gender differences. A text file version of the data is found in the relation link.