Final answer:
A two-tailed hypothesis should be used with an analysis of variance (ANOVA) because it allows for the consideration of differences in either direction. This ensures that all possibilities are taken into account and helps to avoid making incorrect conclusions.
Step-by-step explanation:
When conducting an analysis of variance (ANOVA), a two-tailed hypothesis should be used because it allows for the consideration of the possibility that the means of the groups being compared may differ in either direction.
In a one-tailed hypothesis, only one direction of the difference is considered, which may lead to missing important information or making incorrect conclusions. A two-tailed hypothesis ensures that both possibilities are taken into account.
For example, in an ANOVA comparing the exam scores of students from different math instructors, a two-tailed hypothesis allows us to investigate if there is any significant difference in both higher or lower scores among the instructors.