Crowdsourcing platforms often want to incentivize workers to finish tasks with high quality and truthfully report their solutions. A high-quality solution requires a worker to exert effort; a platform can motivate such effort exertion and truthful reporting by providing a reward. We propose a novel rewarding mechanism based on using a truth detection technology, which can verify the correctness of workers' responses to questions with an imperfect accuracy (e.g., questions regarding whether the workers exert effort finishing the tasks and whether they truthfully report their solutions). We model the interactions between the platform and workers as a two-stage Stackelberg game. In Stage I, the platform optimizes the reward design associated with the truth detection to maximize its payoff. In Stage II, the workers decide their effort levels and reporting strategies to maximize their payoffs (which depend on the output of the truth detection). We analyze the game's equilibrium and show that as the truth detection accuracy improves, the platform should incentivize more workers to exert effort finishing the tasks and truthfully report their solutions. Moreover, our mechanism performs well even when the detection accuracy is not very high. A 60% accurate detection can yield a platform payoff that is more than 85% of the maximum one achieved under perfect (100% accurate) detection.