## Chi-Square Distributions and Goodness of Fit

Read these sections, which discuss chi-square distributions and how to test the goodness of fit. While these sections are optional, studying them may help you if you wish to take the Saylor Direct Credit exam for this course.

### One-Way Tables (Testing Goodness of Fit)

#### Answers

- If all four colors were equally likely to be put in the bag, then the expected frequency for a given color would be
1/4\mathrm{th} of the lollipops. So, the expected frequency would be(1 / 4)(40)=10 . (Of course, this is the theoretical expected frequency, not what we actually expect the bag to look like). - Take the sum of each
\text { (expected - observed) }^{2} / \text { expected }=(10-8)^{2} / 10+(10-5)^{2} / 10+(10-12)^{2} / 10+(10-15)^{2} / 10=5.8