Final answer:
Equal coefficients are not a sign of a double displacement reaction, whereas the formation of a precipitate, the production of gas, or the creation of water are valid signs.
Step-by-step explanation:
The correct answer to the question 'Which is NOT a sign that a double displacement reaction has occurred?' is that the coefficients being equal is not a sign that a double displacement reaction has occurred. A double displacement reaction, also known as a double-replacement reaction, occurs when two ionic compounds exchange ions to form two new compounds, and this process can be verified by observing certain changes.
The potential signs of a double displacement reaction include the formation of a precipitate, the production of gas, or the creation of water. However, the ratio of the coefficients used in the balanced equation does not indicate whether a double displacement reaction has taken place. For a double displacement reaction to occur, one of the products must typically be a solid precipitate, a gas that bubbles out of the mixture, or an insoluble compound like water forming from the reaction.