# Univariate Distributions

• ### Confidence Intervals & Hypothesis Testing

This site explains the relationship between hypothesis testing and confidence intervals.
• ### **Introduction to hypothesis testing -- The z-test

This exercise will help the user understand the logic and procedures of hypothesis testing. To make best use of this exercise, the user should know how to use a z table to find probabilities on a normal distribution, and how to calculate the standard error of a mean. Relevant review materials are available from the links provided. The user will need a copy of the hypothesis testing exercise (link is provided), a table for the standardized normal distribution (z), and a calculator. The user will be asked several questions and will be given feedback regarding their answers. Detailed solutions are provided, but users should try to answer the questions on their own before consulting the detailed solutions. The end of the tutorial contains some "thought" questions.
• ### Normal Distribution JAVA Applet

This applet shades the graph and computes the probability of X, when X is between two parameters x1 and x2. The user inputs the mean, standard deviation, x1 and x2. This applet should be resized for optimal viewing.

• ### Permutations

This program returns a list of all the permutations of the set {1, 2, ..., n}. It allows you to select the given output, copy it, and paste it into a Word or Excel document.
• ### Racing Game Applet

This applet allows the user to simulate a race where the results are based on the roll of a die. The user can determine which player moves forward for a given roll, and can then experiment with the race by determining which player will win more often based on the rules that they specify.

• ### Rocket Launch Probability

This applet is designed to teach an application of probability. This java applet works by simulating a situation where a three stage rocket is about to be launched. In order for a successful launch to occur all three stages of the rocket must successfully pass their pre-takeoff tests. By default, each stage has a 50% chance of success, however, this can be altered by dragging the bar next to each stage.
• ### Central Limit Theorem JAVA Applet

This applet simulates rolling dice to illustrate the central limit theorem. The user can choose between 1, 2, 6, or 9 dice to roll 1, 5, 20, or 100 times. The distribution is graphically displayed. This applet needs to be resized for optimal viewing.

• ### Two Colors Applet

This activity allows the user to simulate pulling red and green balls out of three boxes. The boxes are pre-arranged so that there are two red balls in one box, two green balls in another, and one green and one red ball in the third. The user can shuffle the order of the boxes and the order of the balls in the boxes. To run in single trial mode, click on one of the box to see if the first ball is green. If it is, click on the box again to see if the second ball is green also. A count will be kept of the results. To run in multiple trial mode, enter the number of trials desired in the box and click on the run multiple trials button. This activity would work well in groups of two to three for about twenty minutes if you use the exploration questions provided and ten minutes otherwise.

• ### Simulation of the t-distribution

The t-distribution activity is a student-based in-class activity to illustrate the conceptual reason for the t-distribution. Students use TI-83/84 calculators to conduct a simulation of random samples. The students calculate standard scores with both the population standard deviation and the sample standard deviation. The resulting values are pooled over the entire class to give the simulation a reasonable number of iterations.
• ### Sampling Distributions (Presentation 7)

This PowerPoint presentation teaches sampling distributions related to proportions and means using multiple examples, charts, and graphs.