Large Language Models (LLMs) are increasingly used in Question Answering (QA) chatbots. Using LLMs in QA chatbots enables a more eloquent user conversation, however, these models are far from perfect. A major issue with LLMs is hallucinations, which refer to generated texts that include nonsensical or inaccurate information. These hallucinations are particularly problematic in critical QA contexts such as health or enterprise. Several methods exist to mitigate these hallucinations, wherein the consistency-based hallucination detection techniques are promising as they do not require a ground-truth or deep technical analysis. Although current research has proven the effectiveness of these detection techniques, it does not address possible trade-offs in their real-world use. To close this gap, we conducted a simulation study based on real-world QA data sets to compare different consistency-based hallucination detection techniques and their impact on precision and response time. Our research confirms that more complex detection techniques achieve higher precision, but also lead to a higher response time. In addition, we show that precision and response time strongly depend on the data set used and that precision is only slightly dependent on the consistency determining threshold.