**1. Please download the Apple Runtime for Java available for FREE at (if you already have the Apple Applet Viewer, skip to step 5):**

http://asu.info.apple.com/swupdates.nsf/artnum/n11572

**2. Once the program has downloaded, click on the the MRJ2.2.2.smi icon on your desktop.**

**3. Click on the MRJ Install icon to install the applet viewer. **

**4. Open the Apple Applet Runner Folder**

**5. Click on the Apple Applet Runner Icon**

**6. In the file menu select Open location**

**5. Copy the URL of this page and paste it into the Location box of the Applet Runner window.**

**6. Click Open. The applet may take a moment or two to load.**

**It will be worth your time, I promise!**

**NOTE: You can also save the applet in your Apple Applet Viewer Favorites if you want to access it more quickly next time. Do the following:**

**When the applet is loaded, go to the applets menu and select add applet to list.**

The chi-square test is employed when one whishes to determine if a sample fits some theoretical distribution. The chi-square statistic is calculated as:

where are the observed, and are the expected counts.

Once calculated, the chi-square statistic is compared to a critical value, which is determined using the sample size, the chosen level of significance (typically *a* = 0.05), and a critical value table. If the statistic calculated is less than the critical value, the sample fits the theoretical distribution. Otherwise, there is a significant difference between the observed and expected.

**Adjust the observed and expected counts to the right:**

In this case the critical value doesn't change because the sample size remains constant.