Final answer:
Yes, a chi-square test can be used with ordinal variables that have more than three categories, ensuring that each expected value for a cell is at least five. The test is right-tailed and the chi-square distribution curve becomes more symmetrical as degrees of freedom increase.
Step-by-step explanation:
True, a chi-square test can indeed be used with ordinal variables that have more than three categories. For the test to be valid, some conditions need to be met. Specifically, each observation or cell category must have an expected value of at least five. This ensures that the test results are reliable. The chi-square test is used for various applications including assessing if a data set fits a specific distribution, if two events are independent, and if the variability within a population is as expected.
For example, in a goodness-of-fit test using chi-square, the null hypothesis generally states that the data come from the assumed distribution. The test statistic for a chi-square goodness-of-fit test is large when observed values and the corresponding expected values are not close to each other, indicating that the data may not fit the assumed distribution. It's important to remember that this type of test is right-tailed, and the shape of the chi-square distribution curve can become more symmetrical as the degrees of freedom increase.