Select the appropriate word or phrase to complete the sentence. \[ \text { For the goodness-of-fit test to be valid, each of the } \begin{array}{l}\text { (Choose one) }\end{array} \text { frequencies must be at least } 5 . \] relative ideal expected observed

The appropriate word to complete the sentence is **"expected."** In the context of a goodness-of-fit test, it is essential that the **expected** frequencies in each category are sufficiently large (typically at least 5) to ensure the validity of the test results. This requirement helps to justify the use of the chi-squared approximation. **Completed Sentence:** "For the goodness-of-fit test to be valid, each of the **expected** frequencies must be at least 5." **Answer:** expected