# One Numerical Variable Methods

• ### Analysis Tool: t-Test for Correlated Samples

This calculator returns the value of t for the difference between the means of two correlated samples, for sample sizes up to 10. Users are prompted for sample size as the page opens. It will also calculate various summary statistics for the two samples.

• ### Analysis Tool: Single Sample t-Test

This page will perform a t-test for the significance of the difference between the observed mean of a sample and a hypothetical mean of the population from which the sample is randomly drawn. The user will be asked to specify the sample size as the page opens.

• ### Stock Exchange Game

This activity allows the user to experiment with expected values by changing probabilities and payoffs for two people buying stocks, repeating the experiment up to 100 times. There are links to discussion topics and activities related to the applet.

• ### 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.
• ### 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.

• ### Analysis Tool: Confidence Interval for the Estimated Mean of a Population

Given a sample of N values of X randomly drawn from a normally distributed population, this page will calculate the .95 and .99 confidence intervals (CI) for the estimated mean of the population.

• ### Analysis Tool: Kruskal-Wallis Test for K = 4

As the page opens, you will be prompted to enter the sizes of your several samples. If you are starting out with raw (unranked) data, the necessary rank- ordering will be performed automatically.

• ### Confidence Intervals for Means Applet

This applet simulates finding confidence intervals for the mean of a normal random variable. A sample of size 20 is generated from a standard normal random variable. The blue marks represent the sample data. The sample mean X and sample standard deviation s are found and used to calculate the confidence interval. The black intervals are the confidence intervals which include the true mean 0, and the red intervals are those which exclude 0. This applet needs to be resized for optimal viewing.
• ### Student's t-test Applet

This page gives a short background on Student's t-test and provides three t-test calculators. Two perform t-tests for independent groups and one performs t-tests for matched pairs. Users type in individual data points or copy and paste the entire data set. Some examples are given for demonstration.