Final answer:
The best reason to use a two-tailed hypothesis in ANOVA is because it is too difficult to predict the direction of difference in means when multiple group comparisons are involved, making it necessary to test for any significant difference in both directions.
Step-by-step explanation:
The correct answer is option D: it is too difficult to make predictions for multiple group comparisons in a single statement. In a one-way Analysis of Variance (ANOVA), we compare means across multiple groups to see if at least one of the group means is statistically significantly different from the others.
The test assumes we have normally distributed populations, random and independent samples, equal variances, and a numerical dependent variable.
An ANOVA uses an F-distribution and is inherently a two-tailed test because we are interested in deviations in both directions from the hypothesized mean. The possible outcomes of the hypothesis test either demonstrate that at least one group mean is different or none are different, and there is no specific direction of difference implied. Thus, when multiple comparisons are involved, it is not feasible to predict which group mean will be higher or lower, which justifies the use of a two-tailed hypothesis.