Many recent studies endeavor to improve open-source language models through imitation learning, and re-training on the synthetic instruction data from state-of-the-art proprietary models like ChatGPT and GPT-4. However, the innate nature of synthetic data inherently contains noisy data, giving rise to a substantial presence of low-quality data replete with erroneous responses, and flawed reasoning. Although we intuitively grasp the potential harm of noisy data, we lack a quantitative understanding of its impact. To this end, this paper explores the correlation between the degree of noise and its impact on language models through instruction tuning. We first introduce the Falsity-Controllable (FACO) dataset, which comprises pairs of true answers with corresponding reasoning, as well as false pairs to manually control the falsity ratio of the dataset.Through our extensive experiments, we found multiple intriguing findings of the correlation between the factuality of the dataset and instruction tuning: Specifically, we verified falsity of the instruction is highly relevant to various benchmark scores. Moreover, when LLMs are trained with false instructions, they learn to lie and generate fake unfaithful answers, even though they know the correct answer for the user request. Additionally, we noted that once the language model is trained with a dataset contaminated by noise, restoring its original performance is possible, but it failed to reach full performance.