Channel state estimation-based backoff algorithms for channel access are being widely studied to solve wireless channel accessing and sharing problem especially in super dense wireless networks. In such algorithms, the precision of the channel state estimation determines the performance. How to make the estimation accurate in an efficient way to meet the system requirements is essential in designing the new channel access algorithms. In this paper, we first study the distribution and properties of inaccurate estimations using a novel biased estimation analysis model. We then propose an efficient backoff algorithm based on the theory of confidence interval estimation (BA-CIE), in which the minimum sample size is deduced to improve the contention window tuning efficiency, while a fault-tolerance interval structure is applied to reduce the inaccurate estimations so as to improve the contention window tuning accuracy. Our simulation results show that the throughput of our proposed BA-CIE algorithm can achieve 99% the theoretical maximum throughput of IEEE 802.11 networks, thanks to the improved contention window tuning performance.