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# Algebra level symbolic math

• ### HyperStat Online: Ch. 8 Confidence Intervals

This resource gives a thorough definition of confidence intervals. It shows the user how to compute a confidence interval and how to interpret them. It goes into detail on how to construct a confidence interval for the difference between means, correlations, and proportions. It also gives a detailed explanation of Pearson's correlation. It also includes exercises for the user.

• ### Stats: Sample Size Determination

This resource provides the user with a formula for obtaining sample sizes of a mean and proportion.
• ### HyperStat Online: Ch. 11 Power

This site defines power and explains what factors may affect it, such as significance level, sample size and variance.

• ### **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.
• ### Psychic Test Demonstration

Users 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" the coin by changing the probability of it landing heads.
• ### 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.
• ### Tests of Proportions Applet

In this applet, we simulate a series of hypothesis of tests for the value of the parameter p in a Bernoulli random variable. Each column of red and green marks represents a sample of 30 observations. "Successes'' are coded by green marks and "failures'' by red marks.

• ### 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.