The objective of designing a randomized block experiment is to decrease the within-treatments variation to detect differences between the treatment means.

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This is correct. Randomized block experiments are designed to decrease the within-treatments variation and increase the between-treatments variation, in order to improve the ability to detect differences between the treatment means. This is typically done by grouping individuals into blocks based on some factor that may influence the response (such as age, gender, or baseline level of the outcome), and then randomizing treatments within each block. This helps to control for the influence of the blocking factor and reduce the variability of the response within each block, which in turn improves the power of the test to detect treatment effects.

The Objective of Designing a Randomized Block Experiment Is to Decrease