Final answer:
A large error term in the F-ratio suggests high within-group variance, which can lead to a smaller F-statistic and a larger p-value, indicating the null hypothesis is more likely to be true. Therefore, the statement is True.
Step-by-step explanation:
The question addresses the concept of F-ratio in the context of statistical hypothesis testing, specifically in ANOVA (Analysis of Variance). A larger error term in an F-ratio increases the variability within the groups, which suggests that the differences between group means could be due to random chance rather than a real effect. Thus, a large error term leads to a smaller F-statistic, as the F-ratio is a comparison between the variance between group means and the variance within groups.
If the within-group variance is large, it diminishes the ratio, resulting in a small F-statistic and a larger p-value. This could lead to the failure to reject the null hypothesis, implying the null hypothesis is more likely to be true, supporting the assertion that an F-ratio with a large error term could indicate a greater likelihood of the null hypothesis being true, making the statement True (Option A).