Key Concepts

• The null hypothesis is that the distribution fits the hypothesized proportions. The alternative hypothesis is that the distribution does not fit the hypothesized proportions.
• Expected counts are found by taking the total count and multiplying by each of the hypothesized proportions.
• The expected counts need to be 5 or more to conduct a chi-square test and are NOT rounded to the nearest whole number.
• The degrees of freedom for a chi-square goodness-of-fit test is $k – 1$, where $k$ is the number of categories.
• The chi-square test statistic is the sum of $\frac{(\mathrm{Observed} \ - \ \mathrm{Expected})^2}{\mathrm{Expected}}$ for each category.

Glossary

Chi-square goodness-of-fit: a type of hypotheses test to determine if data is distributed to fit hypothesized proportions