In a one-way ANOVA for a completely randomized design,all other things being held constant,as two sample treatment group means get closer further apart the probability of rejecting the null hypothesis increases.

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As the treatment group means get further apart, the variability between the groups increases, which results in a larger F-statistic and a lower p-value. This leads to an increased probability of rejecting the null hypothesis. Therefore, the statement is true.

In a One-Way ANOVA for a Completely Randomized Design,all Other