This question tests the correct usage of prepositions following the verb 'agitate'. Let's break down the meaning and typical usage.

Understanding the Verb 'Agitate'

The verb 'agitate' has two main meanings:

• To disturb or upset someone mentally.
• To campaign or protest publicly to achieve or change something.

In the given sentence, "The workers agitated ______ better working conditions," the second meaning is relevant. The workers are protesting or campaigning for improvements.

Choosing the Correct Preposition

When 'agitate' is used to mean campaign or protest for a specific goal, the correct preposition to introduce that goal is 'for'. It signifies the reason or objective behind the agitation.

Let's examine the options:

• 'at': This preposition usually indicates a location or a point in time. It doesn't fit the context of advocating for something. For example, "He was agitated at the news."
• 'by': This preposition typically indicates the method or means by which something is done. It doesn't express the goal of the protest. For example, "The change was brought about by the workers."
• 'for': This preposition correctly indicates the purpose or goal of the workers' actions. They were campaigning for better working conditions.
• 'to': This preposition is usually followed by a verb (in its infinitive form) or indicates direction. It doesn't fit grammatically here. For example, "They agitated to improve conditions." (Here 'to improve' is a verb phrase).

Conclusion

The most appropriate preposition to complete the sentence and indicate the objective of the workers' protest is 'for'. The completed sentence reads: "The workers agitated for better working conditions." This structure clearly shows what the workers were demanding.