Final answer:
Each expected frequency in a chi-square goodness-of-fit test must be at least 5 to ensure the test is valid and to maintain the reliability of the chi-square distribution approximation.
Step-by-step explanation:
The question pertains to the minimum expected frequency in each cell for conducting a chi-square goodness-of-fit test. According to the guidelines for the chi-square distribution, each expected frequency in a goodness of fit test must be at least 5. This criterion ensures that the chi-square approximation is valid. If the expected values are less than 5, then the test may not be appropriate or may require a different approach like data pooling to increase the expected values.
The goodness-of-fit hypothesis test compares observed values against expected values to determine whether a data set conforms to a particular distribution. For a proper application of the chi-square test, the rule is that each expected value for observed occurrences (or cell category) must be at least five to ensure the approximation to the chi-square distribution is reliable.